The probability of a point within an equilateral triangle with side 1-unit lying outside its in-circle (inscribed circle) is
(a) 1 - 1 2 3                   (b) 1 - π 3 3                (c) 1 - π 2 3                (d) 1 - 2 π 3 3

Dear Student ,
Please find below the solution to the asked query :

Area of equilateral triangle = 34a2=3412=34 sq. unitRadius of in-circle of an equilateral triangle=36a=36 1=36 unitsArea of in-circle=πr2=π362=3π36=π12 Sq. unitsArea inside equilateral triangle but outside its incircle=Area of equilateral triangle - Area of in-circle= 34 - π12 sq. unitsProbability  point within an equilateral triangle with side 1-unit lying outside its in-circle =Area inside equilateral triangle but outside its incircleArea of equilateral triangle=34 - π1234=1 - π33Correct option is b .
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