In the given figure ABC is right angle triangle, right angled at B. A semi -circle is drawn inside the triangle. Find the radius of semicircle if AO = 4cm & OC = 5cm?
(a) 15/√41
(b) 20/√41
(c) 25/√41
(d) 30/√41
Sol:
∆ADO ~ ∆OEC
∴ in ∆ADO, sinθ = r/4
and in ∆OFC, cosθ = r/5
Now, sin²θ + cos²θ = 1
=>r2/16+r2/25=1
=>r2=16*25/41
=>r=4*5/√41=20/√41
