Question

if OA.OB=OC.OD then show that A=C and B=D​

Answer 1

Answer:

Hence proved...

Step-by-step explanation:

OA . OB = OC . OD.

Show that ∠A =∠C and ∠B =∠D.

OA . OB = OC . OD (Given)

So, OA/OC=OD/OB .... (1)

Also, we have ∠AOD =∠COB (Vertically opposite angles) ...... (2)

Therefore, from (1) and (2), ΔAOD ~ ΔCOB (SAS similarity criterion)

So, ∠A = ∠C and ∠D =∠B

(Corresponding angles of similar triangles)