The angle bisectors A L and B Q in the right triangle <mi mathvariant="normal"

Marquis Cooper

Marquis Cooper

Answered question

2022-06-03

The angle bisectors A L and B Q in the right triangle A B C with A C B = 90 and catheti 15 and 20 divide the median C M into three segments. Find their lengths.

I am not sure how to approach the problem. The most "obvious" thing that we can do is to find the hypotenuse c = a 2 + b 2 = 25 of the triangle A B C. Therefore, m c = 1 2 25 = 12.5. On my sketch A C = 15and B C = 20. What to do next?

Answer & Explanation

bygeroerdxgim

bygeroerdxgim

Beginner2022-06-04Added 1 answers

Let C M A L = { P } and B Q C M = { T }.

Thus,
C P P M = A C A M
and
C T T M = B C B M .
Can you end it now?

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