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.

Answer 1

Proof:

In ∆OMR and ∆ONR,

seg RM ≅ seg RN [Tangent segment theorem]

seg OM ≅ seg ON [Radii of the same circle]

seg OR ≅ seg OR [Common side]

∴ ∆OMR ≅ ∆ONR [SSS test of congruency]

{∴ ∠MRO ≅ ∠NRO

∠MOR ≅ ∠NOR } [c.a.c.t.]

∴ seg OR bisects ∠MRN and ∠MON.