ABCD is a quadrilateral such that ∠D = 90°. A circle with centre O touches the sides AB, BC, CD and DA at P, Q, R and S, respectively. If BC = 40 cm, BP= 28 cm and CD = 25 cm, then what is the radius of the circle?

13 cm

We have,

∠BDS = 90°

BC = 40 cm,

BP = 28 cm

CD = 25 cm

∠ORD = 90°

∠OSD = 90° 

∠DSO = 90°

Now,  DROS is square

⇒ DR = SO (SO is radius)

PB = 28 cm

⇒ QB = 28 (tangent from a same point)

⇒ QC = 12, DC = 25 

⇒ RC = 12 (tangent from a same point),

⇒ DR = 13 cm DS = 13 cm (DR = DS) (tangent from a same point) 

⇒ DR = 13 cm