Math PFMC: Section 1.1 (Brief Reminder of Basic Geometry)

Math: Primer for Mathematics Competitions

Prove the pythagorean theorem.

Prove the sine rule.

Prove the cosine rule.

Prove that the subtended angle at the circumference is half the subtended angle at the centre, consecutively proving that angles at subtended by the same arc at the circumference are equal

Prove that the angle in the semicircle is a right angle

Prove that opposite angles in a cyclic quadrilateral are equal

Prove that the tangents to the circle from exterior points are equal

Prove that there is a unique incircle for each triangle

Prove Alternate Segment Theorem

Prove that the perpendicular bisector of a chord passes through its centre

Prove