Prove that the angle in a segment greater than a semi-circle is less than a right angle.

To do:

We have to prove that the angle in a segment greater than a semi-circle is less than a right angle.

Solution:

Let in a segment $ACB$ greater than a semicircle with centre $O$ $\angle ACB$ is inscribed.

Join $OA$ and $OB$.

Arc $ADB$ subtends $\angle AOB$ at the centre and $\angle ACB$ at the remaining part of the circle.

Therefore,

$\angle ACB =\frac{1}{2}\angle AOB$

$\angle AOB

This implies,

$\angle ACB

$\angle ACB

Hence $\angle ACB

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Updated on: 10-Oct-2022

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