In triangle abc,angle BAC is 22 degrees. A circle with centre O has AB produced,AC produced and BC tangents. Find the number of degrees in angle BOC.

Question

In triangle abc,angle BAC is 22 degrees. A circle with centre O has AB produced,AC produced and BC tangents. Find the number of degrees in angle BOC.

I am not able to interpret it. Plz help me in making the figure.!

Answer 1

I will use words, yes, pretty ridiculous!

Draw triangle $ABC$ like this. Draw $BC$ as a horizontal line segment. Put the point $A$ somewhere above that line segment.

Extend $AB$ "downward,", also extend $AC$ downward. Now imagine drawing a circle in the chunk BC, touching $BC$ from below, and touching $AB$ and $AC$ extended.

This is one of the excircles of $\triangle ABC$. Look at the Wikipedia article on excircles. It has the nice picture that I am unable to supply. And a lot of useful additional information. In Wikipedia's picture, the excircle you are asked about is vaguely north-east of $\triangle ABC$.

Remark: Now you have the picture. If after a serious attempt at solving the problem, you need a hint, please leave a message.