1. Given a fixed point P inside a circle with center O. Two perpendicular chords AB and CD intersect at P (points A, B, C and D are on the circle). E is the symmetric point of P with respect to AC while F is the symmetric point of P with respect to BD. Prove that OE = OD.
2. Given a fixed point P inside a circle with center O and two perpen-dicular chords AB and CD intersecting at P (points A, B, C and D are on the circle). E is the symmetric point of P with respect to AC, and AE cuts the circle at J. Prove that EJ = BP.
Silicon Valley Math University 