In a right-angled triangle ABC, angle C = 90 degrees, angle B = 25 degrees.

| December 28, 2020 | education

In a right-angled triangle ABC, angle C = 90 degrees, angle B = 25 degrees. At what angle is each side visible from the center of the circle circumscribed about the triangle?

The diameter of a circle circumscribed about a right-angled triangle coincides with the hypotenuse, which means that side AB is visible at an angle of 180 °.
The center of the circle O lies in the middle of the hypotenuse AB, which means that OS = OA = OB (circle radii).
Consider a triangle BOA: OS = OB, which means the triangle is isosceles, angle OBC = angle OSB = 25 °. The VOS angle is 180 – (25 + 25) = 130 °.
The BC side is visible from the center of the circle at an angle of 130 °.
Angle A is 180 – (25 + 90) = 65 °.
Consider a triangle AOC: OA = OC, an isosceles triangle, angle OAC = angle OCA = 180 – (65 + 65) = 50 °.
The AC side is visible from the center of the circle at an angle of 50 °.



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