A circle is inscribed in angle C with a magnitude of 40 ° that touches the sides of the angle at points A and B point O
| November 23, 2020 | education
A circle is inscribed in angle C with a magnitude of 40 ° that touches the sides of the angle at points A and B point O – the center of the circle, find the angle AOB?
The radius of the circle is perpendicular to the tangent at the tangent point, so the angles CAO and OBC are 90 °. The sum of the angles of the quadrilateral is 360 °, therefore:
∠AOB = 360 ° – 90 ° – 90 ° – 40 ° = 140 °.
Answer: the angle AOB is 140.
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