Answer:
π/(3√3)
Step-by-step explanation:
The probability = area of circle/ area of triangle
Assuming the triangle has a unit lengths, it's area= 1/2bh = 1/2x1x√3/2=√3/4
Note: the height,h =√(1²-(1/2)²)=√3/4=√3/2
Area of circle = πr²= π(1/2√3)²=π/12
Note: To get the radius of the circle
(√3/2-r)²=r²+(1/2)²
3/4+r²-r√3=r²+1/4
3/4-1/4=r√3
1/2=r√3
r= 1/2√3
Prob = area of circle/ area of triangle=(π/12)/(√3/4)=π/(3√3)
