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If H is the orthocentre of triangle ABC,...

If H is the orthocentre of triangle ABC, R = circumradius and `P = AH + BH + CH`, then (a) `P = 2 (R + r)` (b) max. of P is 3R (c) min. of P is 3R (d) `P = 2 (R -r)`

A

`P = 2 (R + r)`

B

max. of P is 3R

C

min. of P is 3R

D

`P = 2 (R -r)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`AH = 2R cos A, BH = 2R cos B, CH = 2R cos C`
`:. P = 2R (cos A + cos B+ cos C)`
`= 2R (1+(r)/(R))`
`=2 (R + r)`
We know that in any triangle, `r le(R)/(2)`
`:. P le 2R + R`
`rArr P le 3R`
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