# Find the angle ASO if its side CA is tangent to the circle, O is the center of the circle, and the arc AD of the circle enclosed inside this angle is 100 °

May 31, 2020 | Education

| Draw a segment OA.

∠DOA is the central angle for a given circle. It relies on an arc AD equal to 100 °. Therefore, ∠DOA is also equal to 100 °.

∠AOC is adjacent to the DOA corner, therefore ∠AOC = 180 ° – ∠DOA = 180 ° -100 ° = 80 °.

The triangle ACO is rectangular because the radius is always perpendicular to the tangent (by the tangent property). Those. ∠ОАС = 90 °. Using the theorem on the sum of the angles of a triangle, we can write:

180 ° = ∠AСO + ∠CAO + ∠AOC.

∠ACO = 180 ° -∠CO-∠AOC = 180 ° -90 ° -80 ° = 10 °.

Answer: ∠ACO = 10 °

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