A triangle has corners at #(6 , 3 )#, #(1 ,5 )#, and #(2 ,5 )#. What is the radius of the triangle's inscribed circle? Geometry Circles Area of Inscribed Triangle 1 Answer sankarankalyanam Jun 22, 2018 #color(indigo)("Radius of incircle " r = A_t / s = 1.55 / 5.92 ~~ 0.26 " units"# Explanation: #"Incircle radius " r = A_t / s# #A(6,2), B(1,5), C(2,5)# #a = sqrt((1-2)^2 + (5-5)^2) = 1# #b = sqrt((2-6)^2 + (5-2)^2) = 5# #c = sqrt((6-1)^2 + (2-5)^2) = 5.83# #"Semi-perimeter " s = (a + b + c) / 2 = (1 + 5 + 5.83) / 2 = 5.92# #"A_t = sqrt(s (s-a) s-b) (s-c))# #A_t = sqrt(5.92 (5.92-1) (5.92 - 5) (5.92 - 5.83)) = 1.55# #color(indigo)("Radius of incircle " r = A_t / s = 1.55 / 5.92 ~~ 0.26 " units"# Answer link Related questions A triangle has sides with lengths of 4, 6, and 9. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 1, 6, and 2. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 1, 4, and 2. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 6, 4, and 2. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 6, 4, and 3. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 8, 4, and 3. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 8, 4, and 6. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 8, 7, and 6. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 2, 7, and 6. What is the radius of the triangles inscribed circle? A triangle has sides with lengths of 3, 7, and 6. What is the radius of the triangles inscribed circle? See all questions in Area of Inscribed Triangle Impact of this question 1758 views around the world You can reuse this answer Creative Commons License