Question

Explain thales theorem?

Answer 1

Please see below.

Explanation:

Thales theorem states that the diameter of a circle always subtends a right angle on any point on the circle. For example see the following figure.

Here when ends of diameter are joined to any point on the circumference, they all subtend a right angle.

Thales theorem is a corollary of the theorem, which states that the angle subtended by an arc at any point on the circumference is half of the angle subtended by it at the centre.

For example if the arc `AC` subtends angle `/_AOC` at the centre and `/_ABC` any where else on the circumference,

`/_ABC=1/2/_AOC`

and if `AOC` is a diameter, it forms an angle of `180^@` and angle subtended by it at any point on circumference is`1/2xx180^@=90^@`