Seg RM and seg RN are tangent segments of a circle with centre O. Prov

1.	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» 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.

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»

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.

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

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