CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The circumcentre of the triangle with vertices (8,6),(8,-2) and (2,-2) is at the point


A

(2,-1)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

(1,-2)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

(5,2)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

(2,5)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
E

(4,5)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C

(5,2)


Explanation of the correct option:

Finding the circumcentre of the triangle:

Step 1: Equating the circumradius of triangle to find the value of y

Let A(8,6),B(8,-2) and C(2,-2) be the vertices of a triangle.

Let P(x,y) be circumcentre of the triangle.

Then, PA=PB=PC

Now, PA2=PB2.

(x-8)2+(y-6)2=(x-8)2+(y+2)2(y-6)2=(y+2)2y2-12y+36=y2+4y+416y=32y=2

Step 2: Equating the circumradius of the triangle to find the value of x

Similarly, PB2=PC2.

(x-8)2+(y+2)2=(x-2)2+(y+2)2(x-8)2=(x-2)2x2-16x+64=x2-4x+412x=60x=5

Hence, the coordinates of the circumcenter of a triangle is (5,2).

Therefore, option (C) is the correct answer.


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Applications of Differential Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon