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?
Answer & explanation
Correct answer: option 2
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