Circle Geometry Thread (1 Viewer)

shirotaiga · Apr 14, 2016

Hello BOS Community!

I've decided to start a thread solely dedicated to circle geometry questions. Circle geometry is a topic, or a skill rather, I feel requires a lot of practice. A lot of the time these are the questions that completely stop you in your tracks.

Hopefully I will be uploading questions I find challenging quite regularly and encourage anyone who is having trouble or simply wants to practice to do the same! If anyone has a solution please upload it!

I'll start with this one:

ml125 · Apr 14, 2016

shirotaiga · Apr 20, 2016

ml125 said:

Wow!! Great work... helped heaps! I will be posting more soon

shirotaiga · Apr 23, 2016

Sorry for terrible quality

Ambility · Apr 24, 2016

shirotaiga said:
View attachment 33143

View attachment 33144

Sorry for terrible quality

For the first question:
$\\$Construct a line through A and M$\\\angle DAB+\angle DCB=180$ (opposite angles in cyclic quadrilateral)$\\\angle DAN=\angle NAB$ and $\angle DCM = \angle MCB$ (given)$\\2\angle NAB+2\angle MCB = 180\\\angle NAB+\angle MCB = 90\\\angle MAB = \angle MCB$ (subtend same arc)$\\\angle NAB+\angle MAB = 90\\\angle MAN=90\\\therefore $MN is a diameter as it subtends a right angle$$

Circle Geometry Thread (1 Viewer)

shirotaiga

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ml125

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shirotaiga

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shirotaiga

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Ambility

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