0

Guest

Courses New

The equation to the side BC of the triangle ABC is x + 5 = 0. If (-3,2) is the orthocentre and origin is circumcentre , then radius is ?? A √51B √ 13C √53

The equation to the side BC of the triangle ABC is x + 5 = 0. If (-3,2) is the orthocentre and origin is circumcentre , then radius is ?? A √51B √ 13C √53

Grade:12

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
When you ask for the radius of the circle you mean the circumcircle? Is that right? 

The orthocentre, centroid, and circumcentre are collinear, all lying on the Euler line. The centroid divides the line segment from orthocentre to circumcentre in ratio 2:1. Dilate the orthocentre with respect to the circumcentre by scale factor 1/3. The image is the centroid. 

centroid(-1, 2/3) 

Line BC was given (though not actually B or C). Call this line s. The centroid divides all medians in ratio 2:1, being twice as far from each vertex as it is from the opposite midpoint. Dilate line s with respect to the centroid by factor -2. This is its image. 

s': x = 7 

Vertex A must lie on this line. The altitude from A must run through the orthocentre, perpendicular to line s. Point A must also lie on this line, labeled k below. 

k (altitude from A): y = 2 

That gives us A(7, 2). 

The circumradius is the distance from the circumcentre to A. 

circumradius = √(7² + 2²) = √(53)

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More