The triangle ABC is inscribed in a circle centered at the point O. The points O and C lie in the same half-plane relative to the straight line AB. Find the angle ABC if the angle AOB is 167.
Since triangle AOB consists of a chord AB and two radii OA and OB, it is isosceles.
This can be proved if you know that the radii of the circle are always the same.
Then the two remaining corners OAB and OBA will remain:
180 ° – 167 ° = 13 °.
Find the degree measure of the angle OAB and OBA:
13 °: 2 = 6.5 °.
And the degree measure of the angle ABC can be different. It all depends on the position of point C on the circle. But the angle ABC cannot be less than 6.5 °.
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