Inscribed circle

Write the equation of a incircle of the triangle KLM if K [2,1], L [6,4], M [6,1].


x =  5
y =  2
r =  1


k=(66)2+(41)2=3 l=(26)2+(11)2=4 m=(26)2+(14)2=5 p=k+l+m=3+4+5=12 s=p/2=12/2=6 S=k l/2=3 4/2=6   x=(k 2+l 6+m 6)/p=(3 2+4 6+5 6)/12=5k=\sqrt{ (6-6)^2+(4-1)^2 }=3 \ \\ l=\sqrt{ (2-6)^2+(1-1)^2 }=4 \ \\ m=\sqrt{ (2-6)^2+(1-4)^2 }=5 \ \\ p=k+l+m=3+4+5=12 \ \\ s=p/2=12/2=6 \ \\ S=k \cdot \ l/2=3 \cdot \ 4/2=6 \ \\ \ \\ \ \\ x=(k \cdot \ 2+l \cdot \ 6+m \cdot \ 6)/p=(3 \cdot \ 2+4 \cdot \ 6+5 \cdot \ 6)/12=5
y=(k 1+l 4+m 1)/p=(3 1+4 4+5 1)/12=2y=(k \cdot \ 1+l \cdot \ 4+m \cdot \ 1)/p=(3 \cdot \ 1+4 \cdot \ 4+5 \cdot \ 1)/12=2
r=S/s=6/6=1 (x5)2+(y2)2=1r=S/s=6/6=1 \ \\ (x-5)^2+(y-2)^2=1

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 2 comments:
Math student
the answers are not proper. steps are missing.

Dr Math
you are right. The coordinates of the incenter are the weighted average of the coordinates of the vertices, where the weights are the lengths of the corresponding sides.


Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Looking for a statistical calculator?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  2. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  3. Equation of circle
    circle_analytics find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
  4. Circle - AG
    circle2 Find the coordinates of circle and its diameter if its equation is: ?
  5. Find the 12
    circle_eq Find the equation of the circle with center (3,7) and circumference 8π units.
  6. Chord BC
    tetiva2 A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
  7. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  8. Center
    circle Calculate the coordinates of the circle center: ?
  9. Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  10. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  11. Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  12. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  13. ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  14. Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  15. Medians and sides
    taznice3 Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
  16. Euklid4
    euclid_2 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
  17. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?