In the figure given alongside, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle

Question

In the figure given alongside, the rectangle at the corner measures 10 cm × 20 cm. Corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?

(a) 10 cm 

(b) 40 cm 

(c) 50 cm 

(d) None of these

Answer 1

Answer : (c) 50 cm

Draw the perpendicular OP and AQ as shown in the figure and join the points A and O, where O is the centre of the circle. 

OA² = (AQ² + OQ²) = (DQ – DA)² + (OP – QP)² 

⇒ r² = (r – 10)² + (r – 20)² 

(∵ CP = DQ = OP = OA = radius of circle = r) 

⇒ r² = r² – 20r + 100 + r² – 40r + 400

⇒ r² – 60r + 500 = 0 

⇒ (r – 10) (r – 50) = 0

⇒ r = 10, 50 but r > 10 

∴ r = 50 cm.