Multiple choice

If P is a point outside a circle with centre O, and it is 14 cm away from the centre and a secant PAB drawn from P intersects the circle at the points A and B such that AP = 10 cm and BP = 16 cm. Then what is the diameter of circle ?

  1. 13 cm

  2. 10 cm

  3. 12 cm

  4. 11 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the power of a point theorem for secant PAB: PA × PB = PT², where PT is the tangent length. Given PA = 10 cm and PB = 16 cm, we get PT² = 10 × 16 = 160. Since PO = 14 cm (distance from center to P), and PT² + r² = PO² for a tangent, we have r² = 14² - 160 = 36, so r = 6 cm. Therefore, the diameter is 12 cm.

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