A triangle ABC is inscribed in a circle, and the bisectors of the angle ∠A, ∠B and ∠C meet the circumference at X, Y, Z respectively. The angles of the triangle X, Y, Z are respectively
Question
A triangle ABC is inscribed in a circle, and the bisectors of the angle ∠A, ∠B and ∠C meet the circumference at X, Y, Z respectively. The angles of the triangle X, Y, Z are respectively
Solution
The angles of the triangle XYZ are 90° - A/2, 90° - B/2, and 90° - C/2 respectively.
Here's the step-by-step explanation:
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The angle bisectors of a triangle intersect the circumcircle at points that form another triangle, in this case XYZ.
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The angles of triangle XYZ are related to the angles of the original triangle ABC. Specifically, each angle of triangle XYZ is equal to 90° minus half the corresponding angle of triangle ABC.
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Therefore, the angles of triangle XYZ are 90° - A/2, 90° - B/2, and 90° - C/2 respectively.
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