Geometric Constructions

A similar triangle has corresponding sides

A similar triangle has corresponding sides in the same proportion and corresponding angles equal. The construction is done for two cases: when vertice

A line perpendicular to the radius

A line perpendicular to the radius at its outer end is a tangent to the circle. If CP is a radius and P lies on the circle, then line l through P and

Here the tangent is found by

Here the tangent is found by using angle relations. The tangent-secant angle theorem gives ∠CAB ≅ ∠BCD, and the converse of the tangent-secant theorem

If OA and OB are radii

If OA and OB are radii, then OA ⟂ line PA and OB ⟂ line PB. Triangles OAP and OBP are right-angled triangles with OP as the common hypotenuse. A circl

An angle inscribed in a semicircle

An angle inscribed in a semicircle is a right angle. That is why the circle drawn with diameter OP helps identify the tangency points on the given cir