In triangle abc,point0 is the incenter ad=2',ab=10'.and bc =12' find y? would the answer be 5'
To find the length of side AC (denoted as y), we can use the property that the incenter is equidistant from the three sides of the triangle. This means that the distance from the incenter (point O) to each side is equal to the length of the line segment from the incenter to the point where the angle bisector intersects each side.
In this case, line segment AO is equal to line segment DO (where D is the point where the angle bisector intersects side AB), and line segment BO is equal to line segment EO (where E is the point where the angle bisector intersects side BC).
Since AO = DO and BO = EO, we can say that AO + EO = AO + DO = AD. Hence, we have AO + EO = AD.
Given that AD = 2 units, we can substitute and write AO + EO = 2 units.
We also know that AO + BO = AB. Since AB is given as 10 units, we can write AO + BO = 10 units.
From the previous equations, we have AO + EO = 2 units and AO + BO = 10 units.
Subtracting the equations, we get (AO + BO) - (AO + EO) = 10 units - 2 units, which simplifies to BO - EO = 8 units.
Since BO = BC = 12 units (as given) and EO = y, we have 12 units - y = 8 units.
Solving for y, we can subtract 8 units from both sides: 12 units - 8 units = y.
Therefore, y = 4 units.
So, the answer for y is 4 units, not 5 units.