Tangent at A, angle between the tangent and AB 65°, find the angle ACB

Step by step

The question

Question: the line A T touches the circle at A, the angle between it and the chord A B is 65°: find angle A C B.

1 Use the rule

The angle between the tangent and the chord A B is 65°.

The alternate segment theorem: it equals the angle at C, on the other side of the chord, in the alternate segment.

So angle A C B is 65°.

Careful!

Not the angle at B, next to the tangent angle.

The equal angle is across the chord, at C.

2 Check

Let's check: both angles stand on the same chord A B, from opposite sides of it.

So they are equal: 65°.

So it is right!

Let's look back.

First: use the rule.

Last: check.