A triangle has corners at $(5, 2)$ $(5 , 2 )$ , $(4, 7)$ $(4 ,7 )$ , and $(5, 6)$ $(5 ,6 )$ . What is the radius of the triangle's inscribed circle?

Question

A triangle has corners at $(5, 2)$ $(5 , 2 )$ , $(4, 7)$ $(4 ,7 )$ , and $(5, 6)$ $(5 ,6 )$ . What is the radius of the triangle's inscribed circle?

1 Answer

Impact of this question

2694 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-20T05:47:23

$Radius of incircle r = \frac{A_{t}}{s} = 0.4 units$ $color(green)("Radius of incircle " r = A_t / s = 0.4 " units"$

Explanation:

![http://mathibayon.blogspot.com/2015/01/http://derivation-of-formula-for-radius-of-incircle.html](https://useruploads.socratic.org/tJxrUQbRPS2AxwcUMf6J_incircle%20radius.png)

$Incircle radius r = \frac{A_{t}}{s}$ $"Incircle radius " r = A_t / s$

$A (5, 2), B (4, 7), C (5, 6)$ $A(5,2), B(4,7), C(5,6)$

$a = \sqrt{{(4 - 5)}^{2} + {(7 - 6)}^{2}} = \sqrt{2}$ $a = sqrt((4-5)^2 + (7-6)^2) = sqrt2$

$b = \sqrt{{(5 - 5)}^{2} + {(6 - 2)}^{2}} = 4$ $b = sqrt((5-5)^2 + (6-2)^2) = 4$

$c = \sqrt{{(5 - 4)}^{2} + {(2 - 7)}^{2}} = \sqrt{26}$ $c = sqrt((5-4)^2 + ( 2-7)^2) = sqrt26$

$Semi-perimeter s = \frac{a + b + c}{2} = \frac{\sqrt{2} + 4 + \sqrt{26}}{2} = 5.27$ $"Semi-perimeter " s = (a + b + c) / 2 = (sqrt2 + 4 + sqrt26) / 2 = 5.27$

$A_{t} = \sqrt{s (s - a) s - b} (s - c))$ $"A_t = sqrt(s (s-a) s-b) (s-c))$

$A_{t} = \sqrt{5.27 (5.27 - \sqrt{2}) (5.27 - 4) (5.27 - \sqrt{26})} = 2.1$ $A_t = sqrt(5.27 (5.27-sqrt2) (5.27 - 4) (5.27 - sqrt26)) =2.1$

$Radius of incircle r = \frac{A_{t}}{s} = \frac{2.1}{5.27} = 0.4 units$ $color(green)("Radius of incircle " r = A_t / s = 2.1 / 5.27 = 0.4 " units"$

Science

Math

Humanities

... and beyond

A triangle has corners at $(5, 2)$ $(5 , 2 )$ , $(4, 7)$ $(4 ,7 )$ , and $(5, 6)$ $(5 ,6 )$ . 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 (5,2)(5 , 2 ), (4,7)(4 ,7 ), and (5,6)(5 ,6 ). What is the radius of the triangle's inscribed circle?

1 Answer

Explanation:

Related questions

Impact of this question

A triangle has corners at $(5, 2)$ $(5 , 2 )$ , $(4, 7)$ $(4 ,7 )$ , and $(5, 6)$ $(5 ,6 )$ . What is the radius of the triangle's inscribed circle?