perplexus.info :: Geometry : Angle Bisectors and Midpoint Intersection

Angle Bisectors and Midpoint Intersection (Posted on 2024-09-29)

Let ABC be a triangle such that AB=13, BC=12 and CA=5. Let the angle bisectors of A and B intersect at I and meet the opposing sides at D and E, respectively. The line passing through I and the midpoint of DE meets AB at F. What is AF?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 2

After using the half-angle tangent formula to determine CD = 10/3 and CE = 12/5

From there I jumped to coordinates A=(5,0), B=(0,12), C=(0,0).

D=(0,10/3), E=(12/5,0), midpoint M=(6/5,5/3)

I=(2,2)

line MI = y=(5/12)x + 7/6

which intersects AB = y=(-12/5)x+12 at point F=(50/3,36/13)

AF=3

https://www.desmos.com/calculator/qcbeyibe1e

Posted by Jer on 2024-09-29 11:58:19

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