Question

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.

Answer 1

To Prove: Seg OR bisects ∠MRN as well as ∠MON

Proof: In ΔMRO and ΔNRO

seg OM ≅ seg ON   ...[radii of the circle]

seg OR ≅ seg OR    ......[Common side]

seg RM ≅ seg RN    ......[Tangent Segment theorem]

By S.S.S. Test

∴ ΔMRO ≅ ΔNRO

∴ ∠MOR ≅ ∠NOR

∴ ∠MRO ≅ ∠NRO

∴ seg OR bisects ∠MRN and ∠MON.