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

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

Find the dimensions of the largest rectangle that can be inscribed in a semi circle of radius r cm.

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.

Angle in a semi - circle is . . . . . . . .

State and prove angle bisector theorem.

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle alpha is one-third that of the cone and the greatest volume of cylinder is (4)/(27) pi h^(3) tan^(2) alpha .

What happen if the angle in the circle segment is right angle? What kind of segment do you obtain? Draw the figure and give reason.

Prove that the area of a regular polygon hawing 2n sides, inscribed in a circle, is the geometric mean of the areas of the inscribed and circumscribed polygons of n sides.