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AP EAMCET20225 Jul 2022Evening ShiftMathematicsProperties of TrianglesActual

The vertices of a triangle are A(0,0), B(0,2) and C(2,0) , then find the distance between its orthocentre and circumcentre.

Options

  1. A0
  2. B2 units
  3. C1 2 units
  4. D3 units

Correct answer

B. 2 units

Step-by-step solution

Given A(0,0), B(0,2) C(2,0) , A C is a horizontal line and A B is a vertical line. Given, vertices of A B C are the vertices of right-angled triangle, right-angled at A . In a rightangled triangle, A is orthocentre and mid-point of B C is D ( 2+0 2 , 0+2 2 )=(1,1) , which is the circumcentre. Required distance =A D= (1-0)^2+(1-0)^2 = 2 units.

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