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Two circles of radii 4 cm and 9 cm respectively touch each other externally at a point and a common tangent touches them at the points P and Q respectively. They the area of a square with one side PQ, is (SSC CGL 1st Sit. 2012)
- a)97 sq. cm
- b)194 sq. cm
- c)72 sq. cm
- d)144 sq. cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two circles of radii 4 cm and 9 cm respectively touch eachother extern...
r1 + r2 = 13 cm
r2 – r1 = 9 – 4 = 5 cm
∴ Area of square of side PQ = 12 × 12 = 144 sq. cm.
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Two circles of radii 4 cm and 9 cm respectively touch eachother extern...
Given:
- Two circles with radii 4 cm and 9 cm respectively.
- The circles touch each other externally at point T.
- A common tangent to the circles touches them at points P and Q.
- We need to find the area of a square with one side PQ.
To solve this problem, we can follow these steps:
Step 1: Draw a diagram
- Draw two circles with radii 4 cm and 9 cm.
- Mark the point of tangency as T.
- Draw the tangent line passing through T and label the points of contact with the circles as P and Q.
Step 2: Identify the relevant properties
- The radii of the circles are 4 cm and 9 cm.
- The line PT is tangent to the circle with radius 4 cm, and the line QT is tangent to the circle with radius 9 cm.
- The common tangent line PQ is the side of the square we need to find the area of.
- The line joining the centers of the circles is perpendicular to the common tangent line PQ.
Step 3: Find the length of the common tangent PQ
- Since the line joining the centers of the circles is perpendicular to the common tangent line PQ, and the circles touch each other externally, we can use the Pythagorean theorem to find the length of PQ.
- The length of the line joining the centers of the circles is the sum of the radii, which is 4 cm + 9 cm = 13 cm.
- Since the line joining the centers is perpendicular to the common tangent line, we can consider it as the hypotenuse of a right-angled triangle, with the lengths of the radii as the other two sides.
- Using the Pythagorean theorem, we can find the length of PQ as √(13^2 - (9-4)^2) = √(169 - 25) = √144 = 12 cm.
Step 4: Find the area of the square
- The side length of the square is PQ, which we found to be 12 cm.
- The area of a square is given by the formula side length^2, so the area of the square is 12^2 = 144 cm^2.
Therefore, the correct answer is option D) 144 sq. cm.
- Two circles with radii 4 cm and 9 cm respectively.
- The circles touch each other externally at point T.
- A common tangent to the circles touches them at points P and Q.
- We need to find the area of a square with one side PQ.
To solve this problem, we can follow these steps:
Step 1: Draw a diagram
- Draw two circles with radii 4 cm and 9 cm.
- Mark the point of tangency as T.
- Draw the tangent line passing through T and label the points of contact with the circles as P and Q.
Step 2: Identify the relevant properties
- The radii of the circles are 4 cm and 9 cm.
- The line PT is tangent to the circle with radius 4 cm, and the line QT is tangent to the circle with radius 9 cm.
- The common tangent line PQ is the side of the square we need to find the area of.
- The line joining the centers of the circles is perpendicular to the common tangent line PQ.
Step 3: Find the length of the common tangent PQ
- Since the line joining the centers of the circles is perpendicular to the common tangent line PQ, and the circles touch each other externally, we can use the Pythagorean theorem to find the length of PQ.
- The length of the line joining the centers of the circles is the sum of the radii, which is 4 cm + 9 cm = 13 cm.
- Since the line joining the centers is perpendicular to the common tangent line, we can consider it as the hypotenuse of a right-angled triangle, with the lengths of the radii as the other two sides.
- Using the Pythagorean theorem, we can find the length of PQ as √(13^2 - (9-4)^2) = √(169 - 25) = √144 = 12 cm.
Step 4: Find the area of the square
- The side length of the square is PQ, which we found to be 12 cm.
- The area of a square is given by the formula side length^2, so the area of the square is 12^2 = 144 cm^2.
Therefore, the correct answer is option D) 144 sq. cm.
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Two circles of radii 4 cm and 9 cm respectively touch eachother externally at a point and a common tangent touches them at the points P and Q respectively. They the area of a square with one side PQ, is (SSC CGL 1st Sit. 2012)a)97 sq. cmb)194 sq. cmc)72 sq. cmd)144 sq. cmCorrect answer is option 'D'. Can you explain this answer?
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Two circles of radii 4 cm and 9 cm respectively touch eachother externally at a point and a common tangent touches them at the points P and Q respectively. They the area of a square with one side PQ, is (SSC CGL 1st Sit. 2012)a)97 sq. cmb)194 sq. cmc)72 sq. cmd)144 sq. cmCorrect answer is option 'D'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Two circles of radii 4 cm and 9 cm respectively touch eachother externally at a point and a common tangent touches them at the points P and Q respectively. They the area of a square with one side PQ, is (SSC CGL 1st Sit. 2012)a)97 sq. cmb)194 sq. cmc)72 sq. cmd)144 sq. cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CGL 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles of radii 4 cm and 9 cm respectively touch eachother externally at a point and a common tangent touches them at the points P and Q respectively. They the area of a square with one side PQ, is (SSC CGL 1st Sit. 2012)a)97 sq. cmb)194 sq. cmc)72 sq. cmd)144 sq. cmCorrect answer is option 'D'. Can you explain this answer?.
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