In figure, quadrilateral ABCD is circumscribing a circle with centre O and AD ⊥ AB. If radius of incircle is 8 cm, RC = 29 cm and BC is 35 cm. Then find the value of AB.

Option 1 : 14 cm

**Given: **

Quadrilateral ABCD is circumscribing a circle

Radius of incircle = 8 cm

RC = 29 cm

BC = 35 cm

**Concept used:**

The length of tangents drawn from an external point on a circle is equal.

Radius of circle is perpendicular to its tangent.

**Calculation:**

The length of tangents drawn from an external point on a circle is equal.

RC = QC = 29 cm

BC = BQ + QC

⇒ 35 cm = BQ + 29 cm

⇒ BQ = 35 - 29 = 6 cm

QB = PB = 6 cm .....(1)

Radius of circle is perpendicular to its tangent.

AS = OS = PO = AP

OS = 8 cm

⇒ AS = AP = 8 cm ....(2)

AB = AP + PB

⇒ AB = 8 cm + 6 cm = 14 cm

∴ The measurement of AB is 14 cm.

The correct option is 1 i.e.14 cm.