Where is the circumcentre located in any right triangle? Write a coordinate proof of this result.

 

The correct answer is: Hence, circumcentre of right angle triangle lie on midpoint of hypotenuse.

Answer:

• Step by step explanation: 
  • Step 1:
  • Let triangle ABO,

where,

O = (0, 0)

A = (2a, 0)

B = (0, 2b).

• Step 1:
• Let triangle ABO, where:

The midpoint of BC is given by,


So, the perpendicular bisector will intersect BC at M (a, b).
Equation of line BC is

And point M (a, b) satisfy above equation

b = b
Hence, point M (a, b) lies on BC.

• Final Answer: 

Hence, circumcentre of right angle triangle lie on midpoint of hypotenuse.