Find the angle

Geometry Level 4

Let D D be the point on the base B C BC of an isosceles triangle A B C ABC with A B = A C AB=AC and m ( B A C ) = 8 0 ∘ m(BAC)=80^\circ , such that B D : D C = 2 : 1 BD : DC = 2 : 1 , and let P P be the point on the segment A D AD such that m ( B A C ) = m ( B P D ) m(BAC) = m(BPD) . Find m ( D P C ) m(DPC) in degrees.


The answer is 40.

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Soumava Pal by Soumava Pal , 22, India

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1 solution

Soumava Pal
Apr 5, 2016

Here is my solution:

17 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it solving trigonometric equations. Which obviously cannot be done without a computer. But this "human solution" is really awesome. Whoever discovered this deserves some cookies.

Soutik Banerjee - 5 years, 1 month ago

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Give me some cookies. :p

Soumava Pal - 5 years, 1 month ago

I also had pretty much the same solution. Awesome problem keep posting more.

Aditya Kumar - 5 years, 2 months ago

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Thanks. :)

Soumava Pal - 5 years, 2 months ago

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