ABCD is a quadrilateral such that angle D=90degree. A circle with centre O and radius r touches the sides AB,BC,CD and DA at P,Q,R and S respectively. If BC=38 cmCD=25cm and BP=27 cm find r

Given: ABCD is a quadrilateral such that ∠D=90°. 

BC=38 cm,CD=25cm and BP=27 cm

∴From the figure, 

BP=BQ=27 cm [Tangents from an external point]

BC= 38

⇒BQ+QC=38

⇒27+QC=38

⇒QC=38-27

⇒QC=11 cm

∴QC=11 cm=CR [Tangents from an external point]

CD=25 cm

CR+RD=25

⇒11+RD=25

⇒RD=25-11

⇒RD=14cm

Also, 

RD=DS =14cm

:.OR and OS are radii of the circle.
From tangents R and S, ∠ORD = ∠OSD= 90°
Now, ORDS is a square.

:.OR=DS=14 cm

Thus, radius , r = 14cm