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Circumradius of DeltaABC is 3 cm and its...

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 _____

Text Solution

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The correct Answer is:
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`
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Knowledge Check

  • The semi-perimeter of a triangle exceeds its three sides by 5 cm, 3 cm and 2 cm respectively .Then the perimeter of the triangle is

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