Question

If a line intersects two concentric circles (circle with the same center) with center o at a,b,c, and d, prove that ab=cd

Answer 1

Given 2 concentric circles with the same centre O

To prove : AB =CD

Construction: Draw OM perpendiculer to CD

PROOF: OM perpendiculer to CD

Therefore, AM=DM ➡️equation 1

BOTH THE CIRCLES HAVE THE SAME CENTRE

Therefore, BM=CM➡️equation 2

Subtracting equation 2 from 1

AM - BM = DM - CM

=> AB = CD ,HENCE PROVED.....