Problem
GEO-B1-M05-P016 A Tangent Parallel to a Side
#16
★★★☆☆ Level 3 of 5
In triangle \(ABC\), the tangent to the circumcircle at \(A\) is parallel to side \(BC\). Prove that \(AB=AC\).
Compare the angle between the tangent and \(AB\) with angles \(B\) and \(C\).
By the tangent-chord theorem, the angle between the tangent and \(AB\) equals \(\angle ACB\). Since the tangent is parallel to \(BC\), the same angle equals \(\angle ABC\). Hence \(\angle ABC=\angle ACB\), so \(AB=AC\).
Shows how a tangent creates an isosceles triangle.