Proofs In Plane Geometry Properties Of Circles1. tan. rad. 2. rt. in semicircle 3. s in same seg. 4. at centre = 2 at circ. 5. s in opp. seg. () 6. tan. from ext. pt. Congruent & Similar Triangles Midpoint TheoremIf and are the midpoints of and respectively, then // and . Tangent-Chord Theorem (Alternate Segment Theorem)If is a tangent to the circle at , then and .