MathDB

5

Part of 1999 Akdeniz University MO

Problems(2)

geometry

Source:

1/31/2016
A circle centered with OO. CC is a stable point in circle. A chord [AB][AB], parallel to OCOC.Prove that, [AC]2+[BC]2[AC]^2+[BC]^2 is stable.
geometry
geometry

Source:

1/31/2016
Let CC is at a circle. [AB][AB] is a diameter this circle. DD is a point at [AB][AB]. Perpendicular from CC to [AB][AB]'s foot on the [AB][AB] is EE, perpendicular from AA to [CD][CD]'s foot on the [CD][CD] is FF. Prove that, [DC][FC]=[BD][EA][DC][FC]=[BD][EA]
geometry