Question

In the given figure, PA, PB and QR are tangents to a circle. If perimeter of the △PQR = 18 cm, the length of tangent PA is:

Options

• 18 cm

• 27 cm

• 9 cm

• none of these

Answer 1

9 cm

Explanation:

Let tangent QR intersect circle at point D.

Given,

Perimeter of the △PQR = 18 cm.

⇒ PQ + QD + RD + PR = 18   ....(1)

We know that,

Two tangents drawn to a circle form an exterior point are equal in length.

∴ PA = PB = x (let), RD = RA and QD = QB.

Substituting above values in equation (1), we get:

⇒ PQ + QB + RA + PR = 18

⇒ PB + PA = 18

⇒ x + x = 18

⇒ 2x = 18

⇒ x = 9 cm.

∴ PA = 9 cm.