In a circle, a chord is 5 cm away from the centre. If the radius of the circle is 13 cm, what is the length Class 9
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In a circle, a chord is 5 cm away from the centre. If the radius of the circle is 13 cm, what is the length Class 9
Question 1.
In a circle, a chord is 5 cm away from the centre. If the radius of the circle is 13 cm, what is the length of the chord? Class 9
Solution:
Radius of circle = OA = 13 cm
Distance of chord from centre = OM = 5 cm
In right-angled ∆OMA
OA² = OM² + MA²
...[By Baudhayana-Pythagoras theorem]
∴ 13² = 5² + MA²
∴ 169 = 25 + MA²
∴ MA² = 169 - 25
∴ MA = 144
∴ MA = 12 cm
Since the perpendicular from the centre of a circle to a chord bisects the chord.
∴ AB = 2 × MA = 2 × 12 = 24 cm
∴ The length of the chord is 24 cm.