Question

Prove that the line of centres of two intersecting circles equal angles at the two point of intersection.

Answer 1

Data: Two circles having centers $A$ and $B$, intersect at $C$ and $D$.
To prove: $\angle ACB=\angle ADB$.
Construction: Join $A$ and $B$.
Proof: In $\Delta ABC$ and $\Delta ABD$,
$AC=AD$ ($\therefore$ radii of same circle are equal)
$BC=DD$
$AB$ is common.
$\therefore \Delta ABC\cong \Delta ABD$(SSS Postulate.)
$\therefore \angle ACB=\angle ADB$.