The perimeter of ΔABC is 27 cm and its side, BC = 12 cm. AD is the bisector of ∠BAC, while I is the incentre. AI : ID is equal to.
Answer & explanation
Correct answer: option 1
Perimeter of ΔABC = AB + BC + CA = 27 cm
and BC = 12cm
Here,
AB + BC + CA = 27 cm
AB + 12 + CA = 27 cm
AB + CA = 27 - 12 = 15
We know that,
AI : ID = (AB + AC) : BC
= (15) : 12
= 5 : 4
AI : ID = 5 : 4