Question

Two column proof:

If a kite is inscribed in a circle, then one of the diagonals of a kite is a diameter of the circle.

Detailed explanation please, I want to be able to understand this thoroughly.

Diagram is attached, thanks in advance!

Answer 1

Given : BRDG is a kite that is inscribed in a circle,

With BR = RD and BG = DG

To prove : RG is a diameter

Proof:

Since, RG is the major diagonal of the kite BRDG,

By the property of kite,

∠ RBG = ∠ RDG

Also, BRDG is a cyclic quadrilateral,

Therefore, By the property of cyclic quadrilateral,

∠ RBG + ∠ RDG = 180°

⇒ ∠ RBG + ∠ RBG = 180°

⇒ 2∠ RBG = 180°

⇒ ∠ RBG = 90°

⇒ ∠ RDG = 90°

Since, Angle subtended by a diameter or semicircle on any point of circle is right angle.

⇒ RG is the diameter of the circle.

Hence, proved.