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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.
Solution
To Prove: Seg OR bisects ∠MRN as well as ∠MON
Proof: In ΔMRO and ΔNRO
seg OM ≅ seg ON ...[radii of the circle]
seg OR ≅ seg OR ......[Common side]
seg RM ≅ seg RN ......[Tangent Segment theorem]
By S.S.S. Test
∴ ΔMRO ≅ ΔNRO
∴ ∠MOR ≅ ∠NOR
∴ ∠MRO ≅ ∠NRO
∴ 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 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`]
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