Prove that an angle inscribed in a semi-circle is a right angle using vector method.

By vector method show that , an angle inscribed in a semi - circle is a right angle ,

Prove that ,the greatest rectangle inscribed in a given circle is a square.

The area of the triangle inscribed in a circle of radius 4 and the ratio of its angles in the ratio 5:4:3 is

A(z_1),B(z_2),C(z_3) are the vertices a triangle ABC inscribed in the circle abs(z)=2 internal angle bosector of the angle A meet the circumference again at D(z_4) then prove z_4^2=z_2z_3

Rectangles are inscribed inside a semi-circle of radius rdot Find the rectangle with maximum area.

Let ‘O’ be the centre of a circle, PQ is a diameter, then prove that angle PRQ = 90^@ (OR) Prove that angle in a semi-circle is right angle.

Delta ABC is an acute angle triangle inscribed in a circle in a circle .AD is a diameter of the circle . Two perpendiculars BE and CF are drawn from B and C to AC and AB respectively , which intersect each other at the point G . Prove that BDCG is a parallelogram.

Prove that angles in the same segment of a circle are equal.

Semi-circular angle may or not right angle

Answer any One question : prove that semicirular angle is a right angle.