Question

3.
In the figure below, the rectangle at the corner measures 10 cm x 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?
O
A) 10 cm
B) 40 cm
C) 50 cm
D) 30 cm​

Answer 1

Considering the above fig and using Pythagoras formula:

$\leadsto\tt (r-10)^2+(r-20)^2=r^2\\\tt\leadsto r^2+100-20r+r^2+400-40r=r^2\\\leadsto\tt r^2-60r+500=0\\\leadsto\tt r^2-(10+50)r+500=0\\\leadsto\tt r^2-10r-50r+500=0\\\leadsto\tt r(r-10)-50(r-10)\\\leadsto\tt (r-10),(r-50)=0\\\leadsto\tt r=10,r=50$

r=10 or r=50.

r cannot be 10, so it is 50.

Hence,

radius=50cm