In ` A B C ,P` is an interior point such that `/_P A B=10^0/_P B A=20^0,/_P C A=30^0,/_P A C=40^0` then ` A B C` is isosoceles (b) right angled equilateral (d) obtuse angled

Options

A. isosceles
B. right angled
C. equilateral
D. obtuse angled

Answer

A

Explanation

From `Delta APB, Delta PBC, and Delta PCA`, using sine rule
`(AP)/(sin angleABP) (BP)/(sin anglePCB) .(CP)/(sin angle PAC)`
`= (AP)/(sin anglePCA) .(CP)/(sin anglePBC).(BP)/(sin anglePAB)`
`rArr sin30^(@) .sinx .sin 10^(@) = 2in 20^(@) .sin (80^(@) -x) sin 40^(@)`
`rArr x = 60^(@)`
`:. angle BCA = angle CAB = 50^(@)`
So, `DeltaABC` is an isosceles triangle