Question

Chord AB of a circle when extended meets the tangent to the circle at point P. PT is the tangent touching the circle at point T. If lengths of PT and PB are 6 cm and 4 cm respectively, what is the length of PA?

A) 12 cm B) 11 cm C) 10 cm D) 9 cm

Answer 1

Given:

Lengths of PT and PB are 6 cm and 4 cm respectively.

To find:

The length of PA.

Solution:

1) Let the length of the chord AB is x cm.

So the length of the secant PA will be x+4 cm,

The length of the PB is 4 cm,

and the length of the tangent PT is 6 cm.

2) As per the property of the tangent and secant of the circle:

• PT² = PA × PB

• 6² = (x+4)×4

• 36 = (x+4)×4

• 36/4 = (x+4)

• x+4 = 9

• x = 5

So the length of the secant PA is x+4= 5+4 = 9 cm.

The length of PA is (D) 9 cm.