A triangle has corners at $(4, 1)$ $(4 ,1 )$ , $(2, 6)$ $(2 ,6 )$ , and $(7, 3)$ $(7 ,3 )$ . What is the radius of the triangle's inscribed circle?

Question

A triangle has corners at $(4, 1)$ $(4 ,1 )$ , $(2, 6)$ $(2 ,6 )$ , and $(7, 3)$ $(7 ,3 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Impact of this question

2760 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-18T14:15:42

$" "$
Radius of the Triangle's Inscribed Circle ** $= 1.28$ $= 1.28$ Units**

Explanation:

$" "$
A triangle has vertices at $(4, 1), (2, 6) and (7, 3)$ $(4,1), (2,6) and (7,3)$ .

Plot the points on a Cartesian Coordinate Plane and label them as $A, B and C$ $A, B and C$ respectively.

enter image source here

Measure the magnitudes of the line segments $¯ ¯¯¯¯ ¯ A B, ¯ ¯¯¯¯ ¯ B C and ¯ ¯¯¯¯ ¯ A C$ $bar (AB), bar (BC) and bar (AC)$

enter image source here

Perimeter of the triangle $A B + B C + A C$ $AB + BC + AC$

$\Rightarrow 5.39 + 5.83 + 3.61$ $rArr 5.39 + 5.83 + 3.61$

$\Rightarrow 14.83$ $rArr 14.83$ Units

Semi-Perimeter [ s ] $= \frac{P e r i m e t e r}{2}$ $=(Perimeter)/2$

$\Rightarrow \frac{14.83}{2}$ $rArr 14.83/2$ Units

$\Rightarrow 7.415$ $rArr 7.415$ Units

Next, construct angle bisectors..

These three angle bisectors intersect at a point called Incenter.

enter image source here

Using the Incenter as one point and the three sides $A B, B C and A C$ $AB, BC and AC$ , construct perpendicular lines and mark the points where they intersect the sides of the triangle.

Measure the length of these lines from the Incenter

Construct a Circle, the center being the Incenter and one of the points on the sides as the Radius.

Note that all of them have the same magnitude $1.28$ $1.28$ units.

We can also use the formula given below to find the magnitude of the radius.

$r^{2} = \frac{(s - a) (s - b) (s - c)}{s}$ $r^2 = [ (s-a)(s-b)(s-c) ]/s$

$\Rightarrow r^{2} = \frac{(7.415 - 5.83) (7.415 - 3.61) (7.415 - 5.39)}{7.415}$ $rArr r^2=[(7.415-5.83)(7.415-3.61)(7.415-5.39)]/7.415$

$\Rightarrow r^{2} = \frac{12.21262313}{7.415}$ $rArr r^2 = 12.21262313/7.415$

$\Rightarrow r^{2} = 1.647015931$ $rArr r^2 = 1.647015931$

$\Rightarrow r = \sqrt{1.647015931}$ $rArr r = sqrt(1.647015931)$

$\Rightarrow r \approx 1.283361185$ $rArr r ~~ 1.283361185$

$r \approx 1.28$ $r~~1.28$ Units.

Hence, Radius of the Inscribed circle $\approx 1.28$ $~~1.28$ units.

Hope it helps.

Science

Math

Humanities

... and beyond

A triangle has corners at $(4, 1)$ $(4 ,1 )$ , $(2, 6)$ $(2 ,6 )$ , and $(7, 3)$ $(7 ,3 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A triangle has corners at (4,1)(4 ,1 ), (2,6)(2 ,6 ), and (7,3)(7 ,3 ). What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has corners at $(4, 1)$ $(4 ,1 )$ , $(2, 6)$ $(2 ,6 )$ , and $(7, 3)$ $(7 ,3 )$ . What is the radius of the triangle's inscribed circle?