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Let the vertex of an angle ABC be loca...

Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that `\ /_A B C` is equal to half the difference of the angles subtended by the chords AC and DE at the centre.

Text Solution

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IN `/_\BDC`,
`/_ADC` is the exterior angle.
The measure of an exterior angle is equal to the sum of the remote interior angles. Thus,
`/_ADC=/_DBC+/_DCB`
By inscribed angle theorem,
...
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