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.

Answer 1

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,