If H is the orthocentre of triangle ABC, R = circumradius and `P = AH + BH + CH`, then

Question

If H is the orthocentre of triangle ABC, R = circumradius and `P = AH + BH + CH`, then

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)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

5 views Answered 2023-02-05 15:29