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Question: If coordinates of the vertices of a triangle are (2, 0), (6, 0) and (1, 5) then distance between its...

If coordinates of the vertices of a triangle are (2, 0), (6, 0) and (1, 5) then distance between its orthocentre and circumentre is -

A

4

B

6

C

5

D

None of these

Answer

5

Explanation

Solution

Centroid ŗ (2+6+13,0+0+53)\left( \frac{2 + 6 + 1}{3},\frac{0 + 0 + 5}{3} \right)ŗ(3,53)\left( 3,\frac{5}{3} \right)

For orthocenter equation of line ^r to AB passes through

C (1, 5) is x =1 ...(1)

Eq. of line ^r to AC passes through

B (6, 0) is y = (x – 6) 15\frac{1}{5}

Ž 5y = x – 6 ....... (2) By (1) and (2)

ortho centre ŗ (1, –1)

We known centroid ; divided orthocentre circumcentre in

2 : 1 (internally)

\ circumcentre is (4, 3)

\ distance between orthocentre and circumcentre

= (1−4)2+(−1−3)2\sqrt{(1 - 4)^{2} + ( - 1 - 3)^{2}} = 5