9514 1404 393
Answer:
(a) 75.5
Explanation:
There are two ways you can work this.
Pythagorean theorem
Triangle CMP is a right triangle. CM = AC = 55. CP = CB -PB = 55 -15 = 40. Then length PM can be found from ...
PM² +CP² = CM²
PM = √(CM² -CP²) = √(55² -40²) = √1425 ≈ 37.749
The length MN is twice the length of PM, so is ...
MN = 2×PM = 2×37.349 = 75.498
The length of MN is about 75.5.
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Using chord relationships
The products of the different lengths for the same chord are the same for the crossed chords.
AP×PB = MP×PN
We know MP = PN, so ...
MP = √(AP×PB) = √((55+40)(15)) = √1425
As before, MN = 2×MP = 2√1425
MN ≈ 75.5