Question

42. In the figure. Find the value of AB Where PT = 5cm and PA = 4cm.
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Answer 1

Given :   PT = 5cm and PA = 4cm.

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To Find : Value of AB

Solution:

Let say AB = x  cm

PB = PA + AB  = 4 + x

=> PB = 4 + x   cm

Relation between secant and tangent :  

If a tangent segment and a secant segment are drawn to a circle from an exterior point,

Square of the measure of the tangent segment = product of the measures of the secant segment and its external secant segment.

=> PT² = PB. PA

=> 5² = (4 + x) . 4

=> 25 = 16 + 4x

=> 4x = 9

=> x = 9/4

=>  x  =  2.25 cm

AB = 2.25  cm

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