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Question
Question 47. 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?
Question 47. 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?
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Solution
The correct option is C (c) 50
Answer.47 (c)
(x – 20)2 + (x – 10)2 = x2
x2 + 400 – 40x + x2 + 100 – 20x = x2
x2 – 60x + 500 = 0
x2 – 50x – 10x + 500 = 0
x (x – 50) – 10 (x – 50) = 0
x = 50, x = 10.
Q x cannot be 10. ∴ x = 50.
Answer.47 (c)
(x – 20)2 + (x – 10)2 = x2
x2 + 400 – 40x + x2 + 100 – 20x = x2
x2 – 60x + 500 = 0
x2 – 50x – 10x + 500 = 0
x (x – 50) – 10 (x – 50) = 0
x = 50, x = 10.
Q x cannot be 10. ∴ x = 50.
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