This is a Geometry theorem based on Angles adding up to 180 degrees. It is helpful for Mathematics Olympiad. Try to prove the statement!
Statement: Angles adding up to 180 degrees
ABC be an isosceles triangle with AB = AC. P be a point inside the triangle such that, . Suppose M is the midpoint of BC. Show that
Our first claim is, AB and AC are tangents to the circum circle of BPC (prove this). Also extend AP to meet the circum circle at G again. It is sufficient to show .
Next we claim that IPCO and MPGO are cyclic (how?) .
- as MPGO is cyclic
- as IPCO is cyclic
Also as OP = OC (radii), hence = =