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Vedmedyk [2.9K]
3 years ago
7

In △ABC AL is an angle bisector (L∈ BC ). Point M∈ AB so that LM=AM=BM. Find the angles in △ABC, if AC=2AL.

Mathematics
1 answer:
Alex787 [66]3 years ago
3 0

Since LM = AM, point M must be on the perpendicular bisector of AL. Since AM = BM, BL must be perpendicular to AL. This makes ∆ALC a right triangle with hypotenuse AC twice the length of side AL. Hence ∠LAC = ∠LAB = 60°, and AL is angle bisector, median, and altitude.

ΔABC is isosceles with ∠A = 120°, and ∠B = ∠C = 30°.

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