Question

prove theorem 10. 6 of circle class 9​

Answer 1

Step-by-step explanation:

Given:- AB=CD, Angle OMB=Angle OND (90° each).

To prove:- OM=ON.

Construction:- Join B to O and D to O.

Proof:- In ∆BOM and ∆DON.

1)BO=DO(Radius).

2)BM=DN(AB=CD so, 1/2AB=1/2CD and BM=DN).

3)Angle OMB=Angle OND (90° each).

Hence, ∆BOM congruent to ∆DON by RHS congruence rule.

SO, by (CPCT)=> OM=ON.

{NOTE: In this question equidistant from the centre means OM=ON and we have to make Angle M and Angle N =90°}.