Question

lf a line intersect two concertic circle with centre O at A,B,C and D so prove that AB =CD​

Answer 1

Let a perpendicular OP be dropped at chord AD.

In ΔCPO and ΔBPO

BP = CP (perpendicular from the center divides the chord equally)...1

In ΔAPO and ΔDPO

AP = DP (perpendicular from the center divides the chord equally)...2

from equation 1 and 2

AP - BP = DP - CP

AB = DC

Hence proved!