Q. 225.0( 10 Votes )
Perimeter of a triangle is 32 cm. and area of inscribing circle is 38.5 sq. cm. Let us write by calculating the area of this triangle.
Given: Area of inscribing circle = 38.5 cm2
Let BCD is a triangle of perimeter 32 cm. AB, AD and AC are the internal bisectors of respective angles of the triangle. The three internal bisectors meet at A. Perpendiculars drawn from A on sides BC, CD and DB are AG, AE and AF respectively.
AG = AE = AF
Legth of inner radius of triangle = AG
Let AG be r units.
∵ Area of a circle = πr2
⇒ r = 3.5 cm
Now, Area of ∆BCD = area of ∆BCA + area of ∆DCA +area of ∆BDA
⇒ Area ∆BCD = 56cm2
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