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Question
A circle is inscribed in ∆ABC having sides 8 cm, 10 cm and 12 cm as shown in the figure, Find AD, BE and CF.
Solution
AD = AF = x ...(Tangent of the circle)
BD = BE = y ...(Tangent of the circle)
CE = CF = z ...(Tangent of the circle)
AB = AD + DB
x + y = 12 ...(1)
BC = BE + EC
y + z = 8 ...(2)
AC = AF + FC
x + z = 10 ...(3)
Add (1), (2) and (3)
2x + 2y + 2z = 12 + 8 + 10
x + y + z = `30/2` = 15 ...(4)
By x + y = 12 in (4)
z = 3
y + z = 8 in (4)
x = 7
x + z = 10 in (4)
y = 5
AD = 7 cm, BE = 5 cm and CF = 3 cm
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