Question

what is radius of circle inscribed in a triangle with sides of length 12cm,35cm and 37 cm​

Answer 1

We have to find the radius of inscribed circle in a triangle with sides of length 12cm , 35 cm and 37 cm.

solution : see diagram, let O is the centre of inscribed circle in a triangle ∆ABC.

now from figure,

area of ∆BOC = 1/2 × r × BC = 1/2 × r × 37 cm

area of ∆COA = 1/2 × r × CA = 1/2 × r × 35cm

area of ∆AOB = 1/2 × r × AB = 1/2 × r × 12 cm

now area of ∆AOB = area of ∆AOB + area of ∆BOC + area of ∆COA

⇒area of ∆ABC = 1/2 r × 37 + 1/2 r × 35 + 1/2 r × 12

= 1/2 r (37 + 35 + 12)

= 1/2 r × 84

= 42r

here s = (12 + 35 + 37)/2 = 42 cm

now area of ∆ABC = √{s(s - a)(s - b)(s - c)}

= √{42 × (42 - 12) × (42 - 35) × (42 - 37)}

= √{42 × 30 × 7 × 5}

= √{7 × 6 × 6 × 5 × 7 × 5 }

= 7 × 6 × 5

= 210 cm²

now, 210 cm² = 42 r

⇒r = 5 cm

Therefore the radius of circle is 5cm.

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Answer 2

Answer:

hopefully it's helpful to you!!