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.

Proof: In ∆RMO and ∆RNO,

∠RMO ≅ ∠RNO = 90°   ......[`square`]

hypt OR ≅ hypt OR    ......[`square`]

seg OM ≅ seg `square`    ......[Radii of the same circle]

∴ ∆RMO ≅ ∆RNO      ......[`square`]

∠MOR ≅ ∠NOR

Similairy ∠MRO ≅ `square`    ......[`square`]

Answer 1

Proof: In ∆RMO and ∆RNO,

∠RMO ≅ ∠RNO = 90°   ......[Tangent theorem]

hypt OR ≅ hypt OR    ......[Common side]

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

∴ ∆RMO ≅ ∆RNO      ......[By Hypotenuse side test]

∠MOR ≅ ∠NOR

Similarly ∠MRO ≅ ∠NRO    ......[Corresponding angles of congruent triangles]