A circle with the center ‘O’. A point P is 26 cm away from the center of the circle, and the length of the tangent drawn from the point P to the circle is 10 cm. Calculate the length of the radius of the circle.
Let the radius of the circle be r.
The line from the center O to the point of tangency T (where the tangent meets the circle) is perpendicular to the tangent line PT at the point of tangency. Thus, we have a right-angled triangle OTP, where:
- OT = r (the radius of the circle),
- PT = 10 cm (the length of the tangent),
- OP = 26 cm (the distance from the point P to the center O).
Using the Pythagorean theorem:
OP² = OT² + PT²
Substitute the known values:
26² = r² + 10²
Simplify the equation:
676 = r² + 100
Now, solve for r²:
r² = 676 – 100 = 576
Finally, take the square root of both sides:
r = √576 = 24 cm
Thus, the length of the radius of the circle is 24 cm.
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