Answer:
The ratio for AD:DC is 2:3
Explanation:
The given information are;
The ratio by which point B splits AC as AB:BC = 2:1
The ratio by which point D splits AB as AD:DB = 3:2
Therefore, we have;
The fraction of AC that is equal to AB is given as follows;
AB = 2/(2 + 1) × AC = 2/3 × AC
AB = 2/3 × AC
Similarly
BC = 1/3 × AC
Also the fraction of AB that is equal to AD is given as follows;
AD = 3/(3 + 2) × AB = 3/5 × AB
AD = 3/5 × AB
Therefore, the fraction of AC that is equal to AD is given as follows;
AD = 3/5 × AB = 3/5 × 2/3 × AC = 2/5 × AC
Therefore, DC = (1 - 2/5) × AC = 3/5 × AC
Which gives the ration of AD to DC or AD:DC as being;
AD:DC = 2/5 × AC : 3/5 × AC = 2/5:3/5 = 2:3
The ratio for AD:DC = 2:3.