Question

A triangle has corners at `(7 ,8 )`, `(2 ,3 )`, and `(1 ,4 )`. What is the area of the triangle's circumscribed circle?

Answer 1

Area of the circle = 1.2752

Explanation:

the triangle is a right-angled triangle. The side lengths are `sqrt2,sqrt50 and sqrt52, respectively`
Triangle area (A) = `1/2xxsqrt2xxsqrt50=sqrt100/2=10/2=5`
triangle perimeter (P) = `sqrt2+sqrt50+sqrt52=15.696`
inradius (R)= `2A/P=2xx5/15.696=0.6371`
Area of the circle = `pixxR^2=pixx0.6371^2=1.2752`