The radius of a circle is 12.5 cm and the length of one of its chords is 11 cm. What is the distance of the chord from the centre? (correct to one decimal place)

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Accepted Answer

Given:
- Radius (r) = 12.5 cm
- Length of chord (c) = 11 cm

We need to find the distance (d) of the chord from the center of the circle.

Step 1: Recall that the perpendicular from the center of a circle to a chord bisects the chord.

Step 2: Half of the chord length = 11 / 2 = 5.5 cm

Step 3: Using the right triangle formed by the radius, half chord, and the distance from center to chord:

r^2 = d^2 + (c/2)^2

=> d^2 = r^2 - (c/2)^2

=> d^2 = (12.5)^2 - (5.5)^2

=> d^2 = 156.25 - 30.25 = 126

=> d = sqrt(126) ≈ 11.22497 cm

Step 4: Rounding to one decimal place, d ≈ 11.2 cm

Therefore, the distance of the chord from the center is approximately 11.2 cm.

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