Question

In the given figure , AP is tangent to the circle with centre 0. OA =16 , AP=30 ,AP =30 ,QP =x find x

Answer 1

The value of x is 18.

Explanation:

Given: AP is tangent to the circle with centre 0. $OA=16$ , $AP=30$ , $QP=x$

To find: Find x

Solution:

Consider the attached figure

Here, AP is the tangent, OA, OQ are the radius.

We know that the tangent drawn from an external point is perpendicular to the radius.

So, ΔPAO is a right angled triangle at A.

By using Pythagorean theorem

$OP^{2}=AP^{2} +OA^{2}$

We have, $OA=16$ , $AP=30$. So,

$OP^{2}=30^{2} +16^{2}$

$OP^{2}=900 +256$

$OP^{2}=1156$

$OP=\sqrt{1156}$

$OP=34$

Now, $OP=OQ+QP$

$34=16+x$

$x=34-16$

$x=18$

Hence, the value of x is 18.

Learn more:

Tangents drawn from external point

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