Question 22

If the sides of a triangle are 7, 24, 25, then the distance between its circumcentre and orthocentre of the triangle is

Solution

Since $$7^2 + 24^2 = 49 + 576 = 625 = 25^2$$, the triangle is right angled. Its orthocentre is the right angled vertex and its circumcentre is the mid point of the hypotenuse. The distance between them is the median to the hypotenuse, $$\frac{25}{2} = 12.5$$.

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