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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

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## Answers ( )

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,