IIT JEE , AIEEE Forum - Mathematics , Algebra

Ar2008

a triangle is formed by joining 3 pts taken @ random on a circle. what is the probability of it being acute angled?

abhi3chat

it can be either rt. angled or acute angled..but if it passes thru the centre..then it automatically bcomes a rt. angled triangle

utkarshsingh_91

@abhi3chat
it can even be an obtuse angle.....
i think u must see this

Ar2008

@ d ppl above.....ya acceptd wt d possibilities.of the triangles can b....... bt den how do u choose d reqd vertices is wt i wna kno.

nikita19

consider the circle to be divided in two parts by a diameter

if two points of the triangle are on one side of the circle then for the tringle to be an acute angled triangle the third point must lie on the other part of the circle

limiting case being a rigth angled triangle

draw the diagram and check up...

akhil_o

Select any one point P on the circle.Let PQ be the diameter

Let AB be diameter perpendicular to PQ

If the triangle is to be acute,

the other 2 points lie on the other side of Ab than P.(Limiting 90 degrees at AB)

Probability of both points lying on opposite side of P is

1/2*1/2

=1/4.

I guess this should be the answer,but am unsure.

Pl notify me if u find any mistakes and rate if found useful!

ash_speed

the triangle incribed will b obtuse angled if all the three vertices are in the same one semicircle...
whereas the triangle will b acute of 2 vertices are in the same semicircle and the other vertex is in the other part of the circle ...
using this relation u should b able 2 find the prob.

for 1point to b in either part of a fixed diameter cutting the circle is 1/2..
for 2 points 1/2*1/2=1/4
n the 3rd point not to b in the same part as that of the other 2 points (1-1/4)=3/4
therefore the prob. 1/4*3/4=3/16....
not fully sure
correct me if i m wrong...

Ar2008

@ akhil_o: yup.....no mistake. dts d correct answer.

feynmann

Can u find the probability that a particular angle ( say A ) be acute ?

The answer that I am getting is ( 3/4 ).

Ask & Discuss Questions with Community & Experts