Question

a circle with centre P touches the semicircle at point Q and C having centre O if diameter AB=10,AC=6 then find the radius of the smaller circle

Answer 1

Answer:

let OQ intersects smaller circle at M.

And OM be y.

In ∆OCP,<C =90°

So by Sulba Sutra,

OP²=PC²+OC²

=(y+x)²=x²+1

=(5-x)²=x²+1. ...( •.•OP=OQ-PQ)

=25-10x+x²=x²+1

=25 - 10x=1

=24=10x

=x=2.4