Question

If a point P is 17 cm from the center of a circle of radius 8 cm, then the length of the tangent drawn to the circle from the point P is

• A. 10 cm
• B. 12 cm
• C. 15 cm
• D. 14 cm

Answer 1

The Correct Option is C

We are given a circle with radius 8 cm and a point \( P \) that is 17 cm away from the center of the circle. We need to find the length of the tangent drawn from point \( P \) to the circle. We can use the Pythagorean theorem to solve this. In the right triangle formed by the radius of the circle, the line joining the center \( O \) to the point \( P \), and the tangent from point \( P \) to the circle, we know:
The distance from \( P \) to \( O \) is 17 cm.
The radius of the circle (distance from \( O \) to \( A \)) is 8 cm.
The length of the tangent (from \( P \) to \( A \)) is what we need to find. Let the length of the tangent be \( x \). According to the Pythagorean theorem: \[ x^2 + 8^2 = 17^2. \] \[ x^2 + 64 = 289. \] \[ x^2 = 289 - 64 = 225. \] \[ x = \sqrt{225} = 15 \text{ cm}. \]

The correct option is (C): \(15\ cm\)