CAT 2003 Slot 1 — QA Question 42
Basics of CirclesEasy
In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?
Answer & solution
Correct answer: 50 cm
- A
10 cm
- B
40 cm
50 cm
- D
None of the above
Solution
Consider the figure shown above.
(r − 20)2 + (r − 10)2 = r2
r2 + 400 − 40r + r2 + 100 − 20r = r2
r2 − 60r + 500 = 0
r2 − 50r − 10r + 500 = 0
r × (r − 50) − 10 × (r − 50) = 0
r = 50 or r = 10
But, r cannot be 10.
∴ r = 50
Hence, option (c).