Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
2.3k views
in Straight Lines by (56.3k points)

Find the coordinates of the circumcenter of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also find the circumradius.

1 Answer

0 votes
by (30.5k points)
selected by
 
Best answer

Let A(3, 0), B(-1, -6) and C(4 , -1) be the given points.

Let O(x , y) be the circumcenter of the triangle

Then, OA = OB = OC

OA2 = OB2

(x – 3)2 + (y – 0)2 = (x + 1)2 + (y + 6)2

x+ 9 – 6x + y2 = x2 + 1 + 2x + y2 + 36 + 12y

-8x -12y = 28

2x + 3y = -7 …..(i) [After simplification]

Again,

OB2 = OC2

(x + 1)2 + (y + 6)2 = (x – 4)2 + (y + 1)2

x2 + 2x + 1 + y2 + 36 + 12y = x2 + 16 – 8x + y2 + 1 + 2y

10x + 10y = -20

x + y = -2 …..(ii) [After simplification]

Hence, the circumcenter of the triangle is (1, -3)

Circumradius = distance from any of the given points (say B)

=√[(1 + 1)2 + (-3 + 6)2

= √(4 + 9)

= √13 units

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...