Draw the triangle inscribed in the circle. Call the angle measure and therefore because this is an inscribed angle, we get that the arc measure shown in red, .

If we now use the fact that the arc

If we next use the fact that D is a tangent point and also is an inscribed angle at a point of tangency, then we get to infer that or after simplifying .
But now we can notice that we have two triangles with two matching angles. The two triangles are and . The two matching angles are and . This means that we get to infer by Angle-Angle Theorem that the triangles are similar, but we still need to state the similarity relationship in the right order. It is