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please look at the fig first enter image description here

1) How can you claim that the triangle ABC is same as the triangle PQR? 2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB?

I think i have forgotten some basic concept from geometry.

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Because you've not employed the right angles yet.

The velocity of something moving in a circle is necessarily tangent to the circle at whatever point it lies. That property means that the velocity vector is at a right angle to the radius vector. The radii vectors are AB and AC, and their corresponding velocity vectors are v1 and v2. We know that the angle of the velocity vectors is rotated 90 degrees from their radius vectors, so that means the relative angle between two radii vectors will be preserved in their corresponding velocity vectors.

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