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A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?
(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively
(2) PB = 52/5 cm
(2) PB = 52/5 cm
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A bigger circle (with center A) and a smaller circle (with center B) a...
Steps 1 & 2: Understand Question and Draw Inferences
Given that PT is a tangent to the small circle and PS is a tangent to the big circle.
ΔPTB and ΔPSA are right angled at T and S respectively.
We need to find the length of ST.
Step 3: Analyze Statement 1
(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively.
If we drop a perpendicular BD on side AS, we get:
BDST is a rectangle (since all angles of this quadrilateral are right angles).
Therefore, since opposite sides of a rectangle are equal, SD = BT = 4 cm
This means, AD = 9 – 4 = 5cm
In right triangle ADB, by applying Pythagoras Theorem, we get:
BD2 + AD2 = AB2
That is, BD2 = (9+4)2 – (5)2
BD2 = (13+5)(13-5)
BD2 = 18*8 = 24*32
Therefore, BD = 22*3 = 12
Since opposite sides of a rectangle are equal, ST = BD = 12 cm
Since we have been able to determine a unique length of ST, Statement (1) is sufficient.
Step 4: Analyze Statement 2
(2) PB = 52/5 cm
In right triangle BTP, we know the length of only one side: BP.
In order to find the lengths of the other sides of this triangle, we need one more piece of information – either one of the two unknown angles, or one of the two unknown sides.
Since we don’t have this information, we will not be able to find the lengths of the unknown sides of triangle BTP.
Due to a similar reasoning, we will not be able to find the length of the sides of triangle ASP.
So, we will not have enough information to find the length of ST.
Therefore statement 2 is not sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We have arrived at a unique answer in step 3 above. Hence this step is not required.
Correct Answer: A
Most Upvoted Answer
A bigger circle (with center A) and a smaller circle (with center B) a...
Steps 1 & 2: Understand Question and Draw Inferences
Given that PT is a tangent to the small circle and PS is a tangent to the big circle.
ΔPTB and ΔPSA are right angled at T and S respectively.
We need to find the length of ST.
Step 3: Analyze Statement 1
(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively.
If we drop a perpendicular BD on side AS, we get:
BDST is a rectangle (since all angles of this quadrilateral are right angles).
Therefore, since opposite sides of a rectangle are equal, SD = BT = 4 cm
This means, AD = 9 – 4 = 5cm
In right triangle ADB, by applying Pythagoras Theorem, we get:
BD2 + AD2 = AB2
That is, BD2 = (9+4)2 – (5)2
BD2 = (13+5)(13-5)
BD2 = 18*8 = 24*32
Therefore, BD = 22*3 = 12
Since opposite sides of a rectangle are equal, ST = BD = 12 cm
Since we have been able to determine a unique length of ST, Statement (1) is sufficient.
Step 4: Analyze Statement 2
(2) PB = 52/5 cm
In right triangle BTP, we know the length of only one side: BP.
In order to find the lengths of the other sides of this triangle, we need one more piece of information – either one of the two unknown angles, or one of the two unknown sides.
Since we don’t have this information, we will not be able to find the lengths of the unknown sides of triangle BTP.
Due to a similar reasoning, we will not be able to find the length of the sides of triangle ASP.
So, we will not have enough information to find the length of ST.
Therefore statement 2 is not sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We have arrived at a unique answer in step 3 above. Hence this step is not required.
Correct Answer: A
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A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?
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A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?.
A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?.
Solutions for A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?(1) The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively(2) PB = 52/5 cma)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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