A circle is inscribed in a triangle Abc having sides 8 c.m., 10cm and 12cm. find Ad ,Be,and Cf
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Tangents drawn from an external point to a circle are equal.
⇒ AD = AF, BD = BE, CE = CF.
Let AD = AF = a
BD = BE = b
CE = CF = c
AB = AD + DB = a + b = 8 -------- (1)
BC = BE + EC = b + c = 10 -------- (2)
AC = AF + FC = a + b = 12 -------- (3)
Adding (1), (2) and (3), we get
2 (a + b + c) = 30
⇒ (a + b + c) = 15 -------- (4)
Subtracting (1) from (4), we get c = 7
Subtracting (2) from (4), we get a = 5
Subtracting (3) from (4), we get b = 3
Therefore, AD = a = 5 cm, BE = b = 3 cm, CF = c = 7 cm
⇒ AD = AF, BD = BE, CE = CF.
Let AD = AF = a
BD = BE = b
CE = CF = c
AB = AD + DB = a + b = 8 -------- (1)
BC = BE + EC = b + c = 10 -------- (2)
AC = AF + FC = a + b = 12 -------- (3)
Adding (1), (2) and (3), we get
2 (a + b + c) = 30
⇒ (a + b + c) = 15 -------- (4)
Subtracting (1) from (4), we get c = 7
Subtracting (2) from (4), we get a = 5
Subtracting (3) from (4), we get b = 3
Therefore, AD = a = 5 cm, BE = b = 3 cm, CF = c = 7 cm
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