Question : Prove that if you draw a triangle inside a semicircle, the angle opposite the diameter is 90°. Finding the maximum area, or largest triangle, in a semicircle is very simple. These two angles form a straight line so the sum of their measure is 180 degrees. Qibla compass is a compass design showing clearly that Islam is a direction, and Muslims constitute just one out of the many directions of a compass. Radius AC has been drawn, to form two isosceles triangles BAC and CAD. An angle inscribed in a semicircle is a right angle. Objective To verify that angle in a semicircle is a right angle, angle in a major segment is acute, angle in a minor segment is obtuse by paper folding. An inscribed angle of a semicircle is any angle formed by drawing a line from each endpoint of the diameter to the same point on the semicircle, as shown in the figure below. From These angles are formed by the secants AC and BD and are equal to the half sum of â¦ The Circle Theorem that the Angle in a Semicircle is a Right Angle. The right angle FDB then requires that the y coordinate for B is s i n (Î¸ + Ï / 2) = c o s Î¸ The area of each square is the square of those y coordinates, and thus the sum is (r s i n Î¸) 2 + (r c o s Î¸) 2 Given the identity s i n 2 Î¸ + c o s 2 Î¸ = 1, we can simplify the result to r 2 = 64. The angle in a semicircle is a right angle of \(90^\circ\). If