Question

∆ABC is a right angled triangle woth Angle A=90°.A circle is inscribed in it.The lengths of the sides containing the right angle are 6cm and 8cm.Find the radius of the circle.​

Answer 1

Answer:

Ec =2

Step-by-step explanation:

AB= c=6, AC=b=8, Then BC= a=10

Let,

A(0,0) B(0,6) C(8,0)

Coordinates of Incentre

X ={a•x(A) + b•x(B) + c•x(C)}/(sum of three sides)

X = (10•0 + 8•0 + 6•8)/24= 2

Y={a•y(A) + b•y(B) + c•y(C)}/(sum of three sides)

Y= (10•0 + 8•6 + 6•0)/24 = 2

=>(X,Y)(2,2)

So, radius of circle in 2 units.

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Alternative method,

Suppose incircle touch the triangle of sides BC,CA,AB at D,E,F respectively.

NOW,

AF=AE =x, BD=BF=y, CE=CD=z [tangent on a circle from a fixed point]

AB=6, BC=10, AC=8

So,

x + y= 6

x + z = 8

y + z = 10

Solving these equations we get,

x = 2.

If centre of the circle is C

in AECF Angle of A=E=F=π/3

So, AECF is a square.

So, AF =x=EC=2=radius of the circle.