CAT Exam > CAT Questions > On a triangle ABC, a circle with diameter BC ...
Start Learning for Free
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is
Correct answer is '24'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB...
Let us draw the diagram according to the available information.
We can see that triangle BPC and BQC are inscribed inside a semicircle. Hence, we can say that
In triangle ABC,
Area of triangle = (1/2)*Base*Height = (1/2)*AB*CP = (1/2)*AC*BQ
We can see that triangle BPC and BQC are inscribed inside a semicircle. Hence, we can say that
In triangle ABC,
Area of triangle = (1/2)*Base*Height = (1/2)*AB*CP = (1/2)*AC*BQ
Most Upvoted Answer
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB...
Problem: Given a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is:
Solution:
Step 1: Draw the diagram
Step 2: Find the radius of the circle
The diameter of the circle is BC. Therefore, the radius of the circle is BC/2. Using the Pythagorean theorem, we can find BC as follows:
BC^2 = AB^2 + AC^2
BC^2 = 30^2 + 25^2 = 1625
BC = sqrt(1625)
Radius = BC/2 = sqrt(1625)/2
Step 3: Find the length of AP and AQ
The line AP is a tangent to the circle. Therefore, the radius is perpendicular to AP. Using the Pythagorean theorem, we can find AP as follows:
AP^2 = AB^2 - (radius)^2
AP^2 = 30^2 - (sqrt(1625)/2)^2 = 675/4
AP = sqrt(675)/2 = 5sqrt(3)
Similarly, using the Pythagorean theorem, we can find AQ as follows:
AQ^2 = AC^2 - (radius)^2
AQ^2 = 25^2 - (sqrt(1625)/2)^2 = 625/4
AQ = sqrt(625)/2 = 5
Step 4: Find the length of PQ
PQ is the difference between AP and AQ:
PQ = AP - AQ = 5sqrt(3) - 5 = 5(sqrt(3) - 1)
Step 5: Find the length of BQ
BQ = BP + PQ
BP = CP - CB = 20 - sqrt(1625)/2
BQ = 20 - sqrt(1625)/2 + 5(sqrt(3) - 1)
BQ = 5sqrt(3) - sqrt(1625)/2 + 15
BQ = 24 (approx.)
Solution:
Step 1: Draw the diagram
Step 2: Find the radius of the circle
The diameter of the circle is BC. Therefore, the radius of the circle is BC/2. Using the Pythagorean theorem, we can find BC as follows:
BC^2 = AB^2 + AC^2
BC^2 = 30^2 + 25^2 = 1625
BC = sqrt(1625)
Radius = BC/2 = sqrt(1625)/2
Step 3: Find the length of AP and AQ
The line AP is a tangent to the circle. Therefore, the radius is perpendicular to AP. Using the Pythagorean theorem, we can find AP as follows:
AP^2 = AB^2 - (radius)^2
AP^2 = 30^2 - (sqrt(1625)/2)^2 = 675/4
AP = sqrt(675)/2 = 5sqrt(3)
Similarly, using the Pythagorean theorem, we can find AQ as follows:
AQ^2 = AC^2 - (radius)^2
AQ^2 = 25^2 - (sqrt(1625)/2)^2 = 625/4
AQ = sqrt(625)/2 = 5
Step 4: Find the length of PQ
PQ is the difference between AP and AQ:
PQ = AP - AQ = 5sqrt(3) - 5 = 5(sqrt(3) - 1)
Step 5: Find the length of BQ
BQ = BP + PQ
BP = CP - CB = 20 - sqrt(1625)/2
BQ = 20 - sqrt(1625)/2 + 5(sqrt(3) - 1)
BQ = 5sqrt(3) - sqrt(1625)/2 + 15
BQ = 24 (approx.)
Attention CAT Students!
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer?
Question Description
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer?.
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer?.
Solutions for On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer?, a detailed solution for On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? has been provided alongside types of On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, isCorrect answer is '24'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup