Question : Find the value of $x$ in the given figure where TP (tangent on point T) = 15 cm, PB = 2$x$ + 3 cm, PA = 9 cm.
Option 1: 21 cm
Option 2: 18 cm
Option 3: 15 cm
Option 4: 11 cm
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Correct Answer: 11 cm
Solution :
TP = 15 cm
PB = 2$x$ + 3 cm
PA = 9 cm
If a secant AB and tangent at the point T of a circle intersect at a point T of a circle intersect at a point P outside the circle, then PA × PB = PT
2
9 × (2$x$ + 3) = 15
2
⇒ 2$x$ + 3 = $\frac{225}{9}$ = 25
⇒ $x$ = $\frac{25-3}{2}$ = 11
Hence, the correct answer is 11 cm.
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