Question

The PREPENDCULAR bisectors of the sides of triangle ABC meet at i. Prove that i a = ib = ic

Answer 1

Answer:

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Answer 2

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$\red{Given}$ : In ? ABC; ID, IE, IF are perpendicular bisector of sides BC, AC and AB respectively.

and I is the circumcentre of ? ABC

Now in ? IBD and ? ICD

BD = DC (ID is the bisector of BC)

?IDB = ? IDC = 90° (ID is the perpendicular to BC)

ID = ID (Common)

Thus ? IBD ? ICD (by SAS congruence criterion)

? IB = IC ...... (1)

Similarly

? AIE ? CIE

? AI = IC ......... (2)

from (1) and (2)

IA = IB = IC

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