A person is standing at P outside a circular ground at a distance of $26$ m from the centre of the ground. He found that his distances from the points A and B on the ground are $10$ m (PA and PB are tangents to the circle). Find the radius of the circular ground.

$Circle with tangents from external point P$

Question

A person is standing at P outside a circular ground at a distance of

26

m from the centre of the ground. He found that his distances from the points A and B on the ground are

10

m (PA and PB are tangents to the circle). Find the radius of the circular ground.

$Circle with tangents from external point P$

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Accepted Answer

Step 1: $\angle OAP = 90°$ (radius $\perp$ tangent). In right $	riangle OAP$:
Step 2: $(26)^2 = OA^2 + (10)^2 \Rightarrow 676 = OA^2 + 100 \Rightarrow OA^2 = 576$
Step 3: $OA = \sqrt{576} = 24$ m. $	herefore$ Radius $= 24$ m.

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