Question

24 41: The radius of the incircle of a triangle is and the segments into which one side is divided by the point of contact are 6 cm ana 8 cm. Determine the other two sides of the triangle. he the incontro of APC such that inradius

SSC CGL

Maths

Solution

157

4.0 (1 ratings)

( left.begin{array}{l}6=B P=B F 8=c D=c Eend{array}right} ) SOMETNAC ( O M=O N ) As we know ( Delta=r s=sqrt{s(s-a)(s-b)(s-c)} ) ( hat{A} S=ot alpha(x+6+8) ) ( s=14+x ) ( 4(14+x)=sqrt{(14+x)(x)(6)(8)} ) ( 16(14+x)^{2}=48left(x^{2}+14 xright) ) ( 196+x^{2}+28 x=3 x^{2}+42 x ) ( 2 x^{2}+14 x-196=0 ) ( x^{2}+7 x-98=0 ) ( x^{2}+14 x-7 x-98=0 ) ( x(x+14)-7(x+14)=0 ) ( x=7 quad cos x frac{(-14)}{text { Not possible }} ) ( therefore quad x=7 ) ( x+6, x+8 ) ore other two sides 13,15 are other two sides