Multiple choice

P is a point outside a circle and is 26 cm away from its centre. A secant PAB drawn intersects the circle at points A and B such that PB = 32 cm and PA = 18 cm. The radius of the circle (in cm) is:

  1. 12

  2. 8

  3. 10

  4. 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Power of point P = PA * PB = 18 * 32 = 576. Also, Power = d^2 - r^2, where d=26. 576 = 26^2 - r^2 => 576 = 676 - r^2 => r^2 = 100 => r = 10.

AI explanation

Applying the secant and tangent length identity, the square of the tangent length from an external point equals the product of the external secant length and the total secant length. We set up the equation PT squared equals PA times PB, where PA is 18 cm and PB is 32 cm, resulting in PT squared equaling 576 and PT equaling 24 cm. A right triangle is formed by the tangent line, the radius drawn to the point of tangency, and the line segment connecting the external point to the center. Using the Pythagorean theorem, the radius squared equals PO squared minus PT squared, which is 26 squared minus 24 squared, or 676 minus 576, yielding a radius of 10 cm.

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