Question

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Answer 1

Please refer to video for the diagram.
Let tangents at `A` and `B` intersect at point P.
We know tangent at any point at circle, make an angle of `90^@` with a line at center of circle.
So, here, `/_BAP = /_ABP =90^@`
Then, in `Delta ABP`,
`/_PAB+/+ABP+/_APB = 180^@`
`90+90+/_APB = 180`
`/_APB = 0^@`
As, angle created by two tangents`AP` and `BP` of circle is `0^@`, which means `AB` is parallel to `BP`.