Circumradius of `DeltaABC` is 3 cm and its area is `6 cm^(2)`. If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the

Question

Circumradius of `DeltaABC` is 3 cm and its area is `6 cm^(2)`. If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the

Circumradius of `DeltaABC` is 3 cm and its area is `6 cm^(2)`. If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the sides BC, CA and AB, respectively, then the perimeter of `DeltaDEF` (in cm) is _____

Monjur Alahi

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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 - 4
Perimeter of `DeltaDEF = a cos A + b cos B + c cos C`
`= R [sin 2A + sin 2B + sin 2C]`
`= R [4 sin A sin B sin C]`
`= 4R (abc)/(8R^(3)) = (abc)/(2R^(2)) = (2 Delta)/(R) = 4 cm`

6 views Answered 2023-02-05 15:29