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Gekata [30.6K]
2 years ago
13

Prove: If a chord of a circle has a common end point with a diameter and makes an angle of 30° with it, prove that the distance

from the center to the chord is one-fourth the length of the diameter.

Mathematics
1 answer:
nignag [31]2 years ago
6 0

Step-by-step explanation:

The perpendicular distance between the chord and the center of the circle forms a right triangle with the chord and the radius.  Using trig:

sin 30° = x / (D/2)

sin 30° = 2x / D

1/2 = 2x / D

x = D/4

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