Prove that the line of centres of two interesting circles subtends equal angles at the two points of intersection.

Explanation

Given : Two circles with centers A and B in which intersects each other at C and D.

To prove:`angleACB=angleADB`

construction:Join AC,AD,BD and BC.

Proof: In `triangles` ACB and ADB

AC=AD ( radii of same circles)

BC=BD (radii of same circles)

AB=AB (common)

`therefore` `triangleACB~=triangleADB` (By SSS)

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