Question

While constructing an equilateral triangle or a regular hexagon inscribed in a circle, you may have noticed that several smaller equilateral triangles are formed, like PQR shown in the figure below. Explain why PQR is an equilateral triangle.

Answer 1

Go draw 6 circles around a circle so that this circle's radii are the radii of the 6 new circles, and the 6 circles drawn all intersect each others' centers.

Then, you know a circle is 360 degrees.

360/6 for those 6 circles is 60, so 60 degrees.

if the angle is 60 degrees and the radii of the center circle forming the 60 degree angle are equal, the isosceles triangle is an equilateral.

6 equilaterals make a regular hexagon, which shows the 6 circles.

Answer 2

Answer:

Give: Two Circles with Centers p and Q.

To explain: why ΔPQR is Equilateral triangle

In circle with center P.

PQ is radius.

Also PR is radius

In circle with center Q

PQ again radius

and QR is also radius.

Since PQ is radius of both circle.

⇒ Radius of both circles are equal.

⇒ PQ = QR = PR

Therefore, Δ PQR is an Equilateral Triangle as all sides of this triangle are equal.