# Thread: Circle Theorum

1. ## Circle Theorum

Angle B = 32

find Angle MOC

but how do i find MOC and what is the rule?

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Please note: O IS the centre of the circle
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tri-2.jpg picture by jsmith613 - Photobucket

2. Originally Posted by jsmith613
Angle B = 32
$\color{red} Is\ it\ 32^o\ or \ 37^o\ ?$

find Angle MOC

but how do i find MOC and what is the rule?

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Please note: O IS the centre of the circle
---
tri-2.jpg picture by jsmith613 - Photobucket
AB is a diameter, therefore angle BCA=90 degrees.
Therefore angle CAO is 90-37=53 degrees.
Triangle AOC is isosceles as two sides are radius length.
Therefore angle CAO=angle OCA.
Also side AC is perpendicular to side OM.

Angle CBA=37 degrees, so angle MAO is 90-37=53 degrees.
Therefore angle MCO=53 degrees, angle MOC=37 degrees.

Or angle BCA is 90 degrees.
Angle OMA is 90 degrees, therefore line OM is parallel to side BC.
Hence angle OMA=angle BAC.
Triangle OCA is isosceles and is split into 2 identical right angled triangles.
Therefore angle MOA=angle MOC.