Problem
GEO-B1-M08-P011 A Tangent Parallel to a Side
#11
★★★☆☆ Level 3 of 5
In triangle \(ABC\), the tangent to the circumcircle at \(A\) is parallel to \(BC\). Prove that \(AB=AC\).
Use the tangent-chord theorem.
The angle between the tangent and chord \(AB\) equals \(\angle ACB\). Since the tangent is parallel to \(BC\), the same angle equals \(\angle ABC\). Hence \(\angle ABC=\angle ACB\), so \(AB=AC\).
A good problem on an unexpected choice of a circle method.