Question

Find the length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm.​

Answer 1

Step-by-step explanation:

30cm........ ............

Answer 2

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★ Find the length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm.

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★30 cm

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Let AB be a chord of a circle with centre O and radius 17 cm.

Draw OL ⊥ AB. Join OA.

Then, OL = 8 cm and OA = 17 cm

From the right △OLA, we have

OA² = OL² + AL²

==> AL² = OA² – OL² = [(17)² – (8)²] cm²

= (17+8)(17–8) cm²

==> AL² = √225cm = 15cm

Since the perpendicular from the centre of a circle to a chord bisects the chord, we have

AB = 2 × AL = (2×15) cm = 30 cm