Multiple choice

In the triangle ABC, CH and CM are the lengths of the altitude and median to the base AB. If $a = 10, b = 26, c = 32$, then length HM is:

  1. $5$
  2. $7$
  3. $9$

  4. none of the above
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C Correct answer
Explanation

In a triangle with sides 10, 26, 32, the projection of side b (26) onto c (32) is found using the law of cosines. The distance from the vertex to the foot of the altitude is 18, and the distance to the midpoint is 16. The difference is 9.

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