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Question

# AP is the tangent to the circle with centre O and radius 8 cm . If AB = 9 cm, then find the length of tangent AP.

A
10 cm
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B

8 cm

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C

15 cm

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D
13 cm
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Solution

## The correct option is C 15 cm The tangent at any point of a circle is perpendicular to the radius through the point of contact. ∴AP⊥OP ⇒∠OPA=90∘ and △OPA is a right-angled triangle. OA=OB+AB=8+9=17 cm Now, applying pythagoras theorem in triangle OPA, (OP)2+(AP)2=(OA)2 (AP)2=(OA)2−(OP)2 (AP)2=(17)2−(8)2 (AP)2=225 (AP)=√225 AP=15 cm

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