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Question


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

A
10 cm
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B
13 cm
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C
15 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.
APOP

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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