Question

2 tangents are drawn from a point P to a circle as shown . If PA : AB = 5:2 and the perimeter of triangle APB is 48 cm, the length of PB is:

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Answer 1

Solution:

As the tangents drawn from an external point onto a circle are equal in length,

PA = PB

Given PA:AB = 5:2

Let PA = 5x and AB = 2x

PB = PA = 5x

Given that perimeter of the triangle = 48 cm

AB+PA+PB = 48

2x+5x+5x =48 $\Rightarrow$ x = 4

So the length of side PB = 20 cm.