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

15:7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

15:9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

16:7

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

16:9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 16:7
Let a = 4x, b = 5x and c = 6x. Then,
2s = a+b+c = 15x
$N o w, \frac{R}{r} = \frac{\frac{a b c}{4 Δ}}{\frac{Δ}{s}} = \frac{a b c s}{4 Δ^{2}} = \frac{a b c s}{4 s (s - a) (s - b) (s - c)} = \frac{2 a b c}{(2 s - 2 a) (2 s - 2 b) (2 s - 2 c)} = \frac{2 (4 x) (5 x) (6 x)}{(15 x - 8 x) (15 x - 10 x) (15 x - 12 x)} = \frac{240}{7 \times 5 \times 3} = \frac{16}{7}$

Suggest Corrections

Similar questions

A B C, a : b : c = 4 : 5 : 6

A B C,

a : b : c = 4 : 5 : 6

R : r = 16 : 7

A B C :

\frac{R}{r} = \frac{a b c}{4 s}

△ A B C, R, r, r_{1}, r_{2}, r_{3}

A, B, C

r_{1} : r_{2} : r_{3} = 1 : 2 : 3

Compute each of the following: [4 MARKS]

$(a) 15 + (- 5) + 15 + (- 7)$

$(b) 34 + (- 20) + 16 + (- 10)$

$(c) 32 + 16 + 9 + (- 70)$

$(d) - 3 + (- 2) + (- 5) + 7$

Join BYJU'S Learning Program