Question

In a triangle ABC, a:b:c=4:5:6, then the ratio of circumradius to inradius will be .

• A. 15:7
• B. 15:9
• C. 16:7
• D. 16:9

Answer 1

The correct option is C 16:7

Let a = 4x, b = 5x and c = 6x. Then,
2s = a+b+c = 15x
$Now,\frac{R}{r}=\frac{\frac{abc}{4\Delta }}{\frac{\Delta }{s}}=\frac{abcs}{4{\Delta }^2}=\frac{abcs}{4s(s-a)(s-b)(s-c)}=\frac{2abc}{(2s-2a)(2s-2b)(2s-2c)}=\frac{2\left(4x\right)\left(5x\right)\left(6x\right)}{(15x-8x)(15x-10x)(15x-12x)}=\frac{240}{7\times 5\times 3}=\frac{16}{7}$