Question

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the
bigger circle. BD is a tangent to the smaller circle, touching it at D and
intersecting the larger circle at P on extending. Find the length of AP

Answer 1

Given :-

• Radius of bigger circle = 13 cm
• Radius of smaller circle = 8 cm

To find :-

• Length of AP = ?

Construction :-

Join OD

SOLUTION :-

From the figure, we can consider that BD is a tangent of smaller circle.

By Tangent Perpendicularity Theorem,

OD ⊥ BD

In the bigger circle, AB is a diameter.

We know that Angle in a semicircle is 90°

So, ∠APB = 90°

Now, in ∆PBA and ∆DBO,

• ∠PBA = ∠DBO 【Common angle】
• ∠APB = ∠OBD 【Both are 90°】

By AA similarity

『∆PBA∼∆DBO』

Their corresponding sides are proportional.

→ BA ÷ BO = PA ÷ DO

→ 26 ÷ 13 = AP ÷ 8

→ 2 = AP ÷ 8

→ AP = 8 × 2

∴ AP = 16 cm