Proofs in Plane Geometry - Alternate Segment Theorem

Proofs in Plane Geometry - Alternate Segment Theorem

TGM Original Questions

In the diagram, \(TA\) is the tangent to the circle at \(A\) and \(TB\) is a straight line that intersects the circle at \(B\) and \(D\). \(C\) is a point on \(TB\) such that \(AC\) bisects angle \(BAD\). Prove that

  1. triangles \(TAD\) and \(TBA\) are similar, and
  2. triangle \(TAC\) is an isosceles triangle.

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