Circle And System Of Circles Question 5
Question: The locus of a point which moves such that the sum of the squares of its distances from the three vertices of a triangle is constant, is a circle whose centre is at the
Options:
A) Incentre of the triangle
B) Centroid of the triangle
C) Orthocentre of the triangle
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let a triangle has its three vertices as (0, 0), (a, 0), (0, b). We have the moving point (h, k) such that $ h^{2}+k^{2}+{{(h-a)}^{2}}+k^{2}+h^{2}+{{(k-b)}^{2}}=c $
$ \Rightarrow 3h^{2}+3k^{2}-2ah-2bk+a^{2}+b^{2}=c $ Therefore, $ 3x^{2}+3y^{2}-2ax-2by+a^{2}+b^{2}=c $ Its centre is $ ( \frac{a}{3},\ \frac{b}{3} ) $ , which is centroid of $ \Delta $ .
BETA
