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General

Easy

Question

# If in a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then the radius of the circle DEF is -

- R/2
- 2R
- R
- None of these

Hint:

## The correct answer is: R/2

### Given :-In a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then we have to find the radius of the circle DEF.

## In pedal $△DEF$

$EF=acosA$

$DE=ccosC$

$DF=bcosB$

## If circum-radius of DEF is

$EF=acosA$

$DE=ccosC$

$DF=bcosB$

Therefore, the radius of the circle DEF is R/2.

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