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Help Im bad at geometry
In triangle AB, let the angle bisectors be BY and CZ. Given AB = 16, AY = 16, and CY = 16, find BC and BZ.

 Jun 14, 2023
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To find BC and BZ in triangle AB, we can use the angle bisector theorem.

The angle bisector theorem states that in a triangle, if a line divides one side into two segments, the ratio of the lengths of those segments is equal to the ratio of the lengths of the other two sides.

In triangle AB, let's label BC as "x" and BZ as "y".

According to the angle bisector theorem, we can set up the following ratios:

AY / CY = AB / BC 16 / 16 = 16 / x

Simplifying the equation: 1 = 16 / x

Cross-multiplying: x = 16

So, BC = 16.

Now, let's find BZ using the same theorem:

AY / CZ = AB / BZ 16 / 16 = 16 / y

Simplifying the equation: 1 = 16 / y

Cross-multiplying: y = 16

So, BZ = 16.

Therefore, BC = 16 and BZ = 16 in triangle AB.

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 Jun 15, 2023
edited by ollysuper  Jun 15, 2023

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