A point P is 25 cm away from the center of a circle and the length of tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
Let us consider a circle with center O.
Consider a point P 25 cm away from the center such that OP = 25 cm
A tangent PQ is drawn at point Q on the circle from point P such that PQ = 24 cm
To Find : Length of radius OQ = ?
Now, OQ ⏊ PQ
[Tangent at any point on the circle is perpendicular to the radius through point of contact]
∴ In right - angled △POQ,
By Pythagoras Theorem,
[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2 ]
(OP)2 = (OQ)2 + (PQ)2
(25)2 = (OQ)2 + (24)2
625 = (OQ)2 + 576
(OQ)2 = 49
OQ = 7 cm