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Condition of Concurrency of 3 Straight Lines

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Show that the radii of the three escribed circles of a triangle are the roots of the equation x^{3^{}}-x^2(4R+r)+xs^{2 }-rs^2 =

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Q. Prove that the cubic equation whose roots are the radii

r_{1}, r_{2}, r_{3}

of escribed circles of a triangle is

t^{3} - (r + 4 R) t + s^{2} t - s^{2} r = 0

Q. If the area of a triangle is 96 and the radii of the escribed circles are 8, 12, 24, then the greatest side of the triangle is

Q. If the area of a triangle is

96 s q . u n i t s

and the radii of the escribed circle are

8, 12, 24,

then the perimeter of the triangle is

r_{1}, r_{2}, r_{3}

are the radii of the escribed circles of a triangle

A B C

r

is the radius of its incircle,then

r_{1} r_{2} r_{3} - r (r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1})

Q. If the radius of the circumcircle of a triangle is 10 and that of the incircle is 5, then the square of the sum of radii of the escribed circles is

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Condition of Concurrency of 3 Straight Lines

Standard XII Mathematics

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