sandysilva wrote:
A triangle is inscribed in a circle. A point is randomly chosen inside the circle. What is the probability that point lies on the area common to triangle and circle?
A) Longest side of triangle ABC measures 10.
B) ABC is a right isosceles triangle.
Source:
Experts GlobalSince we are looking at probability, even finding ratio of areas will be sufficient...
Statement I does not say anything about radius of circle or area of triangle..
Insufficient
Statement II states ABC is isosceles right angle triangle....
Remember the rule - any angle in the semicircle with two sides meeting the end of diameter is 90..
So here the Dia of circle is hypotenuse of triangle...
Since triangle is isosceles, sides of triangle and radius are related..
We can find the ratio of two areas..
Sufficient
. B
Otherwise..
Sides of isosceles right angle triangle = Dia/√2 = 2r/√2=√2r
Area of isosceles triangle =\(\frac{1}{2}*√2r*√2r=r^2..\)
Area of circle=\(π*r^2\)..
Probability = \(\frac{r^2}{π*r^2}=\frac{1}{π}\)