Question

Triangle in a semicircle​

Answer 1

Step-by-step explanation:

The angle at vertex C is always a right angle of 90°, and therefore the inscribed triangle is always a right angled triangle providing points A, and B are across the diameter of the circle. ... The area within the triangle varies with respect to its perpendicular height from the base AB.

Assuming the triangle in the middle has a height the radius of the circle and base as the diameter of the circle, you can calculate the area for the triangle by squaring the radius and the area of the remaining semi-circle by doing pi times the radius squared minus two times the radius squared divided by two.

The full arc of a semicircle always measures 180° (equivalently, π radians, or a half-turn). ... By Thales' theorem, any triangle inscribed in a semicircle with a vertex at each of the endpoints of the semicircle and the third vertex elsewhere on the semicircle is a right triangle, with right angle at the third vertex.

Answer 2

Step-by-step explanation:

The triangle ABC inscribe within a semicircle . The angle at vertex C is always at right angle of 90° , and therefore inscribed triangle is always a right angle triangle providing points A, and B are across the diameter of the circle.

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