Given: a circle with a center O. and a triangle ABC. Arc BK = 58 degrees, find the angle A, B, C. angle ABK = 90 degrees.

univerkov | February 3, 2021 | education

1) The triangle ABC inscribed in the circle has a side of AK, which lies on the diameter of the circle AK, since the angle <ABK = 90 °.

2) The ВK arc is measured with a central angle <ВOK = 58 °.

3) Angle inscribed in a circle <ВAK = 1/2 (<ВOK) = 1/2 * 58 ° = 29 °.

4) ВС ⊥ ОВ according to the condition (ВС – tangent), then <ABO = 180 ° – 58 ° = 122 °.

5) <ABO = 180 ° – <BOA – <BAO = 180 ° – 122 ° – 29 ° = 29 °.

6) <ABC = <ABO + <OBC = 29 ° + 90 ° = 119 °.

7) Angles of triangle ABC: <BCA = 180 ° – <BAC – <ABC = 180 ° – 29 ° – 119 ° = 32 °; <BAC = <BAC = 29 °.

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