Question

This diagram is a straightedge and compass construction. A is the center of one circle,
and B is the center of the other. Explain how we know triangle ABC is equilateral.

Answer 1

ABC is a equilateral triangle .

Proof :-

Let's assume both circles as C1 and C2 [ as shown in the figure ]

• AB is the radius of circle C1
• AB is the radius of Circle C2

AC is the radius of circle C1.

BC is the radius of circle C2 .

AB and AC both are radius of circle C1 so both are equal ie AB = AC .

AB and BC both are radius of circle C 2 so both are equal ie AB = BC .

Hence we conclude that .

AB = BC = AC.

So the triangle is equilateral triangle.