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Dissecting Triangles

Dissecting Triangles 1.4 - Solution

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In the diagram, we can see that is the midpoint of and that is the perpendicular to through Therefore, is the perpendicular bisector of

According to the Perpendicular Bisector Theorem, in a plane, if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In our case, is the point on the perpendicular bisector and and are the endpoints. Therefore, according to the theorem,

Since we can write an equation to find Let's solve the equation for
Solve for
We can now find the value by substituting for in the corresponding expression.