Question

Abc is a triangle in which b = 90, bc = 48 cm and ab = 14 cm. A circle is inscribed in the triangle, whose centre is o. Find radius r of in-circle.

Answer 1

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Answer 2

Answer:

Radius, r = 6 cm.

Step-by-step explanation:

Given: Δ ABC is right angled triangle at B as right angle.

           BC = 48 cm , AB = 14 cm

           radius of incircle is r and center is O.

To find: Value of Radius r.

Figure is attached.

In ΔABC

By Pythagoras Theorem,

AC² = AB² + BC²

AC² = 14² + 48²

AC² = 196 + 2304

AC² = 2500

AC = √2500

AC = 50 cm

Now, A, B, C to O and we find r using formula of area,

By figure,

ar Δ ABC = ar Δ AOB + ar Δ AOC + ar Δ BOC

$\frac{1}{2}\times base_1\times height_1=\frac{1}{2}\times base_2\times height_2\,+\,\frac{1}{2}\times base_3\times height_3\,+\,\frac{1}{2}\times base_4\times height_4\\\\\frac{1}{2}\times BC\times AB=\frac{1}{2}\times AB\times r\,+\,\frac{1}{2}\times AC\times r\,+\,\frac{1}{2}\times BC\times r\\\\\frac{1}{2}\times 48\times 14=\frac{1}{2}\times 14\times r\,+\,\frac{1}{2}\times 50\times r\,+\,\frac{1}{2}\times 48\times r$

$24\times 14=7\times r\,+\,25\times r\,+\,24\times r\\\\336 = (7+25+24)\times r\\\\56\times r =336\\\\r=\frac{336}{56}\\\\r = 6\:cm$

Therefore, Radius, r = 6 cm.