Multiple choice

Two tangents AP and AQ are drawn to a circle with centre O from an external point A, where P and Q are points on the circle. If AP=12 cm and ∠PAQ=60, then the length of chord PQ is:

  1. 12 cm

  2. 10 cm

  3. 16 cm

  4. 24 cm
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A Correct answer
Explanation

In a circle, tangents from an external point are equal, so AP = AQ = 12 cm. Triangle APQ is isosceles with AP = AQ = 12 cm and angle PAQ = 60°. Therefore triangle APQ is equilateral since it's isosceles with vertex angle 60°. In an equilateral triangle, all sides are equal, so PQ = AP = AQ = 12 cm.

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