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Tangent Theorem

Tangents para...

Question

Tangents parallel to the three sides of triangle ABC are drawn to its incircle. If x, y, z be the length of the parts of the tangent within the triangle( with respect to sides a,b,c) then find the value of: x/a+y/b+z/c

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Solution

$All three sides of triangle will be the tangent to incircle . So here, x = a, y = b and z = c Hence, \frac{x}{a} + \frac{y}{b} + \frac{z}{c} = \frac{a}{a} + \frac{b}{b} + \frac{c}{c} = 1 + 1 + 1 = 3$

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