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Distances between Special Points in a Triangle

In a right an...

Question

In a right angled triangle PQR, Circumcenter and orthocenter are at a distance of ------ units from each other. (Where R is the circumradius)

A

R

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B

2R

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C

3R

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D

4R

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Solution

The correct option is A
R

We have seen that the distance between circumcenter and orthocenter is = R $\sqrt{1 - 8 c o s A . c o s B . c o s C}$

It is given that the triangle is right angled so, any angle out of three will be 90°.
And cos(90°) = 0
So, the distance will be = R

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