Question
If the perpendicular from a vertex of an equilateral triangle to the opposite side is 15β3 cm, find its inradius.
Solution
ATQ,
Altitude = (β3a/2)
β (β3a/2) = 15β3
β a = 30 cm
Inradius = a / (2β3) = 30 / (2β3) = 15 / β3 = 5β3 cm
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