Angle C of 118 ° is inscribed with a circle that touches the sides of the corner at points

Angle C of 118 ° is inscribed with a circle that touches the sides of the corner at points A and B, point O is the center of the circle. Find the angle AOB.

Consider a triangle ABC: AC = AB (two tangents from one point), which means triangle ABC is isosceles. Therefore, the angle CAB = angle ABC = (180 ° – 118 °): 2 = 31 °.

The OBC angle is 90 ° (the angle between the radius and the tangent).

Find the angle OBA: 90 ° – 31 ° = 59 °.

Consider the ABO triangle: the AO side is equal to the AO side (these are two radii of one circle), which means that the ABO triangle is isosceles. Consequently, the angle ОВА is equal to the angle ОАВ = 59 °.

Let’s find the value of the angle AOB: 180 ° – (59 * 2) = 62 °.

Answer: angle BOA = 62 °.