# Thread: Yes.. another circle theorem

1. ## Yes.. another circle theorem

Hi I am currently stuck on this question
If anybody could tell me how to approach this or offer any help then please post. Here is the question:

Thanks for any help!

SORRY! the point P is the intersection of the chord AC with chord BD

2. You got B and C the wrong way round.

Anyway, the problem is the same as saying that 3×∠BOD = ∠COA.

∆POD is isosceles, so ∠POD = ∠PDO.

∴ ∠OPC = ∠POD + ∠PDO = 2×∠POD

∆COD is isosceles, so ∠OCD = ∠ODC = ∠POD.

∴ ∠COA = ∠OPC + ∠OCD = 2×∠POD + ∠POD = 3×∠POD.

3. Originally Posted by JaneBennet
You got B and C the wrong way round.
Well, if I had noticed that I wouldn't have spent an idle 20 minutes trying to do it! Good spot.

-Dan

4. Thanks Jane!
but why does the labelling of a point matter so much? :S
its just a label

5. Originally Posted by Geometor
Thanks Jane!
but why does the labelling of a point matter so much? :S
its just a label

Because the condition 3 BD = AC will be different for your figure