In the diagram , AOB is a diameter of the circle with centre O . ACX , BDY and DEC are tangents to the circle at A , B and E respectively . Show that

(1) angle COD =90

(2) OC . OD = 1/2 AB . CD

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- November 7th 2009, 06:42 AMthereddevilsgeometry (3)
In the diagram , AOB is a diameter of the circle with centre O . ACX , BDY and DEC are tangents to the circle at A , B and E respectively . Show that

(1) angle COD =90

(2) OC . OD = 1/2 AB . CD - November 7th 2009, 07:22 AMGrandad
Hello thereddevilsPart (1) is like your previous question: Geometry (1). Here's the outline of the proof. I'll leave the details to you. Let .

Then and (congruent 's)

Then look at the quadrilateral . Can you see why ? Hence . Then look at , and you're there.

Part (2) Let .

Then look at the areas: