perplexus.info :: Geometry : Angle hunt inside Isosceles

Angle hunt inside Isosceles (Posted on 2025-05-23)

Consider triangle ABC an isosceles triangle such that AB = BC. Let P be a point satisfying

∠ ABP = 80, ∠ CBP = 20, and AC = BP

Find all possible values of ∠ BCP.

No Solution Yet Submitted by Danish Ahmed Khan

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possible solution

Comment 1 of 1

I think the only possible answer is 130. Call the midpoint of AC=O.

WLOG Let AO=OC=1, AC=2

∠ABC=100

∠BAC=∠BCA=40

∠OBP=30

Drop a perpendicular from P to BO at point D

Since triangle BDP is a 30-60-90 with BP=2, DP=1

and ODPC is a rectangle

∠BCP=90+40=130

Graphed in Desmos to help me see it

https://www.desmos.com/calculator/gv80rgjxwn

Posted by Jer on 2025-05-25 21:05:03

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