Problem
GEO-B1-M05-P013 Two Angles With a Tangent
#13
★★★☆☆ Level 3 of 5
A tangent is drawn at point \(A\) to the circumcircle of triangle \(ABC\). It is known that \(\angle ABC=72^\circ\), \(\angle ACB=43^\circ\). Find the angles between the tangent and chords \(AB\) and \(AC\).
The angle between a tangent and a chord equals the angle standing on that chord.
The angle between the tangent and \(AB\) equals the inscribed angle standing on \(AB\), namely \(\angle ACB=43^\circ\). The angle between the tangent and \(AC\) equals the inscribed angle standing on \(AC\), namely \(\angle ABC=72^\circ\).
Forces the student to choose the correct chord for the tangent theorem.