3. In the given figure, the bisectors of ∠B and ∠C of ∆ABC meet at I. If IP ⊥ BC, IQ ⊥ CA and IR ⊥ AB, prove that i) IP = IQ = IR

Question

3. In the given figure, the bisectors of ∠B and ∠C of ∆ABC meet at I. If IP ⊥ BC, IQ ⊥ CA and IR ⊥ AB, prove that
i) IP = IQ = IR
ii) IA bisects ∠A.

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Charlie 1 month 2021-08-21T13:40:53+00:00 1 Answer 0 views 0

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    2021-08-21T13:42:28+00:00

    Answer:

    Given: IP ⊥BC, IQ ⊥CA and IR ⊥ AB and the bisectors of ∠B and ∠C of ∆ABC meet at I

    To prove: IP=IQ=IR and IA bisects ∠A

    Proof:

    In ∆BIP and ∆BIR we have,

    ∠PBI = ∠RBI …given

    ∠IRB = ∠IPB = 90° …Given

    IB = IB …common side

    Thus by AAS property of congruence,

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