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