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lions [1.4K]
3 years ago
12

In ∆ABC, the median AM (M ∈ BC ) is perpendicular to the angle bisector BK (K ∈ AC ). Find AB, if BC = 12 in. Show with work

Mathematics
1 answer:
otez555 [7]3 years ago
3 0

Call the point where BK intersects AM point X. BX is the altitude of ∆ABM, and it is also the angle bisector of angle ∠ABM. Hence ∆ABM is isosceles, and AB ≅ MB.

M is the midpoint of BC, which is 12 inches long. Hence MB is half that length, or 6 inches.

Since AB is the same length as MB, which is 6 inches, ...

... AB is 6 inches.

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