+456 Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.
+10 Problem: The relationship between these segments isn't straightforward. If BD = BI + DI, then the values don't align because BD = 4, BI = 6, and DI = 3. This shows that B is not directly connected to D through I in a straight line.
Area Calculation: Using the given sides of triangle BID, we calculate the area. The base is BD = 4, and the height is DI = 3. The area formula is:
Area = 1/2 × base × height
Substitute the values: Area = 1/2 × 4 × 3 = 6
Answer: The area of triangle BID is 6.
