a circle is inscribed in a triangle ABC such that the touches the sides ab BC and CA at point B and F respectively if the length of the sides ab BC and CA are 12 centimetre 8cm and 10cm respectively find the length of AD,BD,CF
Answers
Answer:
Step-by-step explanation: Given: AB = 12 cm, BC = 8 cm and AC = 10 cm.
Let, AD = AF = x cm, BD = BE = y cm and CE = CF = z cm
(Tangents drawn from an external point to the circle are equal in length)
2(x + y + z) = AB + BC + AC = AD + DB + BE + EC + AF + FC = 30 cm
x + y + z = 15 cm
AB = AD + DB = x + y = 12 cm
z = CF = 15 - 12 = 3 cm
AC = AF + FC = x + z = 10 cmGiven: AB = 12 cm, BC = 8 cm and AC = 10 cm.
Let, AD = AF = x cm, BD = BE = y cm and CE = CF = z cm
(Tangents drawn from an external point to the circle are equal in length)
2(x + y + z) = AB + BC + AC = AD + DB + BE + EC + AF + FC = 30 cm
x + y + z = 15 cm
AB = AD + DB = x + y = 12 cm
z = CF = 15 - 12 = 3 cm
AC = AF + FC = x + z = 10 cm
y = BE = 15 - 10 = 5 cm
x = AD = x + y + z - z - y = 15 - 3 - 5 = 7 cm