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  • In Fig. (1), ABC is a triangle in which = 90º, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle.&

In Fig. (1), ABC is a triangle in which \angle B= 90º, BC = 48 cm and AB = 14 cm. A circle is inscribed in the triangle, whose centre is O. Find radius r of in-circle. 

 

 
 
 
 
 

Answers (1)

In \: \: \Delta ABC , using Pythagoras theorem 

AC^2 = AB ^2 + BC ^ 2\\\\ AC ^ 2 = (14)^2 + ( 48) ^ 2 \\\\ AC = 50 cm

area of ABC = area of \Delta AOB + area of \Delta BOC

+area of \Delta AOC

= \frac{1}{2} \times b \times h = \frac{1}{2} \times b _1\times h _1+ \frac{1}{2} \times b_2 \times h _2 + \frac{1}{2} \times b_3 \times h _3\\\\ 14 \times 48 = 14 \times r + 48 \times r + 50 \times r \\\\ 56 r = 336 \\\\ r = 336 /56 \\\\ r = 6 cm

Radius r of in circle is 6 cm 

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Safeer PP

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