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

In ∆RMO and ∆RNO,

∠RMO ≅ ∠RNO = 90°   ...\[\boxed{\text{[Tangent theorem]}}\]

hypt OR ≅ hypt OR    ...\[\boxed{\text{[Common side]}}\]

seg OM ≅ seg \[\boxed{\text{ON}}\]   ...[Radii of the same circle]

∴ ∆RMO ≅ ∆RNO   ...\[\boxed{\text{[By Hypotenuse side test]}}\]

∠MOR ≅ ∠NOR

Similarly ∠MRO ≅ \[\boxed{\text{∠NRO}}\]   ...\[\boxed{\text{[Corresponding angles of congruent triangles]}}\]