Circle 1 Question 6

6. Let the orthocentre and centroid of a triangle be A(3,5) and B(3,3), respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is

(a) 10

(b) 210

(c) 352

(d) 352

(2018 Main)

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Answer:

Correct Answer: 6. (c)

Solution:

  1. Key idea Orthocentre, centroid and circumcentre are collinear and centroid divide orthocentre and circumcentre in 2:1 ratio.

We have orthocentre and centroid of a triangle be A(3,5) and B(3,3) respectively and C circumcentre.

Clearly, AB=(3+3)2+(35)2=36+4=210

We know that, AB:BC=2:1

BC=10

Now, AC=AB+BC=210+10=310

Since, AC is a diameter of circle.

r=AC2r=3102=352



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