Question

Find the incentre and excentres of the triangle formed by the points (3, 2), (7,2), (7,5).​

Answer 1

Step-by-step explanation:

formula of incentre of triangle=

Ox=x1+x2+x3/3, Oy=y1+y2+y3/3

so

X=3+7+7/3=17/3

Y=2+2+5/3=9/3=3

REQUIRED COORDINATES = (17/3,3)

Answer 2

The Incentre of a triangle is (6,7/2) and the excentre of a triangle is (28/3,4)

Given:

The set of numbers separated by commas (3, 2), (7,2), (7,5).​

To Find:

The incentre and the excentre of a triangle

Solution:

Consider the points ,

A(3, 2), B (7,2) , C(7,5)

Taking distance formula for,

AB,BC, CA

AB = $\sqrt{(7-3)^2 + 0 } = 4$

BC = $\sqrt{0 - (2-5)^2} = 3$

CA = $\sqrt{(7-3)^2 + (5-2)^2} = 5$

a =3 , b =5 , c= 4

Incentre of a triangle is,

I = $\frac{(9 + 35 + 28}{12},\frac{12+10+20)}{12}$

I = (6, 7/2)

Excentre of a triangle is given by,

I1 = $\frac{-9 + 35 +28}{6} ,\frac{,-6 + 10 + 20}{6}$

I1 = (28/3, 4)

I2 = (1/3, 8/3)

I3 = ( 8/3,-2/3)

Hence, we get the value of the incentre as  (6,7/2)

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