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### Q.5: Secant PAB is drawn from an external point P to a circle with center O, intersecting at A and B. Given OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, find the radius of the circle.

- Using the secant-tangent theorem: \( OP^2 = PA \times PB \)
- \( 17^2 = 12 \times 22.5 \)
- \( 289 = 270 \)
Hence, this setup isn't typical, but assuming calculation approximation might reveal 4,√23 is closed.

A secant PAB is drawn from an external point P to the circle with center at O, intersecting at A and B. If OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, then the radius of the circle is:

This problem involves applying the secant-tangent theorem to find the radius of a circle. Given OP = 17 cm, PA = 12 cm, and PB = 22.5 cm, the radius of the circle is determined through key geometry principles. Suitable for Grade 9-10 students.

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