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

In ∆OMR and ∆ONR,

seg MR = seg NR (Tangent segments drawn from an external point to a circle are congruent)

seg OM = seg ON (Radii of the same circle)

seg OR = seg OR (Common)

∴ ∆OMR ≌ ∆ONR (SSS congruence criterion)

⇒ ∠ORM = ∠ORN (CPCT)

Also, ∠MOR = ∠NOR (CPCT)

∴ seg OR bisects ∠MRN and ∠MON.