ABC triangle with ∣AB∣<∣BC∣<∣CA∣ has the incenter I. The orthocenters of triangles IBC,IAC and IAB are HA,HA and HA. HBHC intersect BC at KA and perpendicular line from I to HBHB intersect BC at LA. KB,LB,KC,LC are defined similarly. Prove that
∣KALA∣=∣KBLB∣+∣KCLC∣ geometrygeometry proposedorthocenterincircle