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5 concurrent angle bisectors wanted, 5 given (2016 From Tasks to Tasks, p3 Ukr)

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May 3, 2021
geometryangle bisectorconcurrencyconcurrent

Problem Statement

In fig. the bisectors of the angles ∠DAC\angle DAC, ∠EBD \angle EBD, ∠ACE\angle ACE, ∠BDA\angle BDA and ∠CEB\angle CEB intersect at one point. Prove that the bisectors of the angles ∠TPQ\angle TPQ, ∠PQR\angle PQR, ∠QRS\angle QRS, ∠RST\angle RST and ∠STP\angle STP also intersect at one point. https://cdn.artofproblemsolving.com/attachments/6/e/870e4f20bc7fdcb37534f04541c45b1cd5034a.png
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