JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Properties of Triangle

If the line

3 x + 4 y - 24 = 0

intersects the

x

-axis at the point

A

and the

y

-axis at the point

B

, then the incentre of the triangle

O A B

, where

O

is the origin, is:

Answer: (B)

Solution

The line

3 x + 4 y - 24 = 0

meets the

x

-axis at

A (8, 0)

and the

y

-axis at

B (0, 6)

, so triangle

O A B

is right-angled at

O

with legs

O A = 8

O B = 6

and hypotenuse

A B = 10

. For a right triangle the inradius is

r = \frac{8 + 6 - 10}{2} = 2

, and because the right angle sits at the origin the incentre is at

(r, r) = (2, 2)

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Single correct option