## Wednesday, March 15, 2023

### Geometry Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures. Difficulty Level: High School.

Geometry Problem 1526. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

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1. https://photos.app.goo.gl/csBRn4k2btFAxqn86

1. https://photos.app.goo.gl/GwyH5jPsyhtGKUD69

Define point I as midpoint of AD and N is the projection of D over AB
Note that AED is the right triangle => IE=IA=ID
Since I is the incenter of triangle AED
Triangle IFE similar to AND ( case AA)
ND=AG=2.EF=20

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3. Let AB, DE extended meet at U. Drop a perpendicular UP to AD, P on AD.

Triangles AEU & AED are congruent ASA & so AU = AD
E is midpoint of DU hence from the midpoint theorem UP = 2 X 10 = 20

Now Triangles APU & ADG are congruent ASA (since AU = AD)
So AG = UP = 20

Sumith Peiris
Moratuwa
Sri Lanka

4. Let K, L be projections of E onto AB, CD, then E being onto the angles bisectors, KE=EF=EL=10, but K-E-L are collinear...