P and Q are centres of two intersecting circles with equal radius. Prove that PQ = QR = PR where R is any point of intersection as shown in the following figure.

For the Circle with Centre P,

Radius = PQ = PR ……(i)

For the Circle with Centre Q,

Radius = PQ = QR ……(ii)

Now from (i) and (ii) we get,

PQ = QR = RQ (By Euclid’s First Axiom)

Euclid’s First axiom: Things which are equal to the same thing are equal to one another.