A point P is 13 cm away from the center of a circle. A tangent is drawn from P to the circle, and its length is 12 cm. What is the area of the circle?
\(25\pi\) cm²
Let the radius be \(r\) and let the point of tangency be \(T\), so \(OT \perp PT\).
Use the right triangle OTP:
\(OP^2 = OT^2 + PT^2\)
\(13^2 = r^2 + 12^2 \;\Longrightarrow\; 169 = r^2 + 144 \;\Longrightarrow\; r^2 = 25 \;\Longrightarrow\; r = 5 \text{ cm}\)
Area of the circle:
\(A = \pi r^2 = \pi (5)^2 = 25\pi \text{ cm}^2\)
Hence the area is \(25\pi\) cm² — option (1).
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