The radius of the given circle with centre O is 5 cm. If OP = 3 cm, then what is the length of chord XY?

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5 cm

6 cm

7 cm

8 cm

answer is D.

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Detailed Solution

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

∴ XP = PY

Let the length of PY be x.

On applying Pythagoras theorem to ΔOPY, we obtain

OY² = OP² + PY²

⇒ (5 cm)² = (3 cm)² + PY²

⇒ 25 cm² = 9 cm² + PY²

⇒ PY² = (25 − 9) cm² = 16 cm²

⇒ PY = 4 cm

∴ XY = XP + PY = 2 PY = 2 (4 cm) = 8 cm

Thus, the length of chord XY is 8 cm.

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