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Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF, which intersect at I. If DI = 3, BD = 4, and BI = 8, then find the area of triangle ABC.

 Feb 9, 2023
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The area of a triangle is given by:

Area = 1/2 x base x height

We have,

A triangle ABC.

Angle bisectors are AD, BE, and CF, which intersect at I.

 

DI = 3

DI = AI = 3

Height of the triangle = AD = AI + DI = 3 + 3 = 6

BD = 4 = BC

Base of the triangle = BC = BD + DC = 4 + 4 = 8

 

The area of a triangle:

= 1/2 x base x height

= 1/2 x 8 x 6

= 1 x 4 x 6

= 24

 

Thus,

The area of the triangle is 24.

 Feb 9, 2023

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