If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

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Solution

Let us first draw whatever is given so that we can understand the problem better.

Since the tangent to a circle is always perpendicular to the radius of the circle at the point of contact, we have drawn OP perpendicular to PQ. Thus we have a right triangle with one of its sides as the radius. To find the radius we have to use Pythagoras theorem.

Therefore the radius of the circle is 7 cm.

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