A certain line intersects parallel lines $a$ and $b$ at points $A$ and $B$ respectively. The bisector of one of the angles formed with vertex $B$ intersects line $a$ at point $C$. Find $A C$, if $A B=1$.

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Prove that triangle $ABC$ is isosceles.

## Solution

Let $D$ be a point on line $b$, lying on the same side of line $AB$ as point $C$. Then $\angle ACB = \angle DBC = \angle ABC$, so triangle $ABC$ is isosceles. Therefore, $AC = AB$.

## Answer

1.