The coordinates of the three vertices of a triangle are: (1,2), (7,2), and (1,10). Then the radius of the incircle of the triangle is

Question

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Solution:

Compute side lengths:

AB = √[(7−1)² + (2−2)²] = √[36 + 0] = 6

AC = √[(1−1)² + (10−2)²] = √[0 + 64] = 8

BC = √[(7−1)² + (2−10)²] = √[36 + 64] = √100 = 10

Semi-perimeter:

s = (AB + BC + AC)/2 = (6 + 10 + 8)/2 = 24/2 = 12

Area (using Heron’s formula or right triangle property):

Triangle is right-angled at A: area = (AB × AC)/2 = (6 × 8)/2 = 24

Incircle radius formula: r = Area / s

r = 24 / 12 = 2

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