In a triangle ABC, the lengths of the sides AB and AC are 17.5 cm
and 9 cm respectively. Let D be the point on the line segment BC
such that AD is perpendicular to BC. If AD = 3cm, then what is
the radius (in cm) of the circle circumscribing the triangle?
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radius of circle is given by,
triangle ABC= abc/4Δ
DC=root(AC²-AD²)
DC=root(9²-3²)
DC=root(81-9)
DC=root(72)
DC=6*root(2)
DC=8.48 cm
BD=root(17.5²+3²)
BD=root(297.25)
BD=17.24 cm
BC=BD+DC
BC=17.24+8.48
BC=25.72 cm
Length of BC is 25.72 cm
Area of triangle =1/2*BC*3
Area=1/2*25.72*3
Area=38.58 cm²
radius=a*b*c/4*area
radius=25.72*17.5*9/(4*38.58)
radius=26.25 cm
so the radius of a triangle is 26.25 cm
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