The probability of a point within an equilateral triangle with side 1-unit lying outside its in-circle (inscribed circle) is (a) - Maths - Probability

Question

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

Rishabh Mittal · Accepted Answer

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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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

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