let-I-be-the-incenter-of-a-non-isosceles-ABC-and-let-the-incircle-be-tanget-to-the-sides-point-D-E-F-the-line-AI-intersects-ABC-at-A-and-S-the-line-SD-intersect

Question Number 224594 by Nicholas666 last updated on 20/Sep/25

$$ \\ $$$$\:\:\:\:\mathrm{let}\:{I}\:\mathrm{be}\:\mathrm{the}\:\mathrm{incenter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{non}−\mathrm{isosceles}\:\:\Delta{ABC}\:\:\:\:\:\: \\ $$$$\:\:\:\:\mathrm{and}\:\mathrm{let}\:\mathrm{the}\:\mathrm{incircle}\:\mathrm{be}\:\mathrm{tanget}\:\mathrm{to}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{point}\:{D},{E},{F}.\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{line}\:{AI}\:\mathrm{intersects}\: \left({ABC}\right)\:\mathrm{at}\:{A}\:\mathrm{and}\:{S}. \\ $$$$\:\:\:\:\:\mathrm{the}\:\mathrm{line}\:{SD}\:\mathrm{intersects}\: \left({ABC}\right)\:\mathrm{at}\:{S}\:\mathrm{and}\:{T}.\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{let}\:{IT}\:\cap\:{EF}\:={M},\: \left({BIC}\right)\:\cap\: \left({DEF}\right)={K},{L}. \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:{KDLM}\:\mathrm{is}\:\mathrm{a}\:\mathrm{kite}. \\ $$$$ \\ $$$$ \\ $$

Commented by Nicholas666 last updated on 20/Sep/25

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