Multiple choice

Two chords of lengths16 cm and 17 cm are drawn perpendicular to each other in a circle of radius 10 cm. The distance of their point of intersection from the centre is approximately

  1. 6.5 cm

  2. 7.2 cm

  3. 7.6 cm

  4. 8 cm
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D Correct answer
Explanation

Let the chords be AB and CD intersecting at P. Let the center be O. The distance of a chord from the center is d = sqrt(r^2 - (L/2)^2). For L=16, d1 = sqrt(100 - 64) = 6. For L=17, d2 = sqrt(100 - 72.25) = sqrt(27.75) = 5.27. If the chords are perpendicular, the distance from the center to the intersection point P is sqrt(d1^2 + d2^2) = sqrt(36 + 27.75) = sqrt(63.75) = 7.98, which is approximately 8.

AI explanation

For the chord of length 16 cm, the perpendicular distance from the center is found using the Pythagorean theorem as the square root of (10^2 - 8^2), which equals 6 cm. For the chord of length 17 cm, its distance from the center is the square root of (10^2 - 8.5^2), which is the square root of 27.75 cm. Because the two chords are perpendicular to each other, the distance of their point of intersection from the center is calculated using the Pythagorean theorem for these two perpendicular distances: the square root of (6^2 + 27.75). This calculates to the square root of 63.75, which is approximately 8 cm.

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