Maths-

General

Easy

Question

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

Hint:

- Distance between two points having coordinates (x1, y1) and (x2, y2) is given by formula:

- Distance =

## 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.

- Step 1:
- Let triangle ABO,

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

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

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