MathDB
Circles are tangent

Source: Greece JMO 2018, pr 4

March 5, 2018
geometrytangent circles

Problem Statement

Let ABCABC with AB<AC<BCAB<AC<BC be an acute angled triangle and cc its circumcircle. Let DD be the point diametrically opposite to AA. Point KK is on BDBD such that KB=KCKB=KC. The circle (K,KC)(K, KC) intersects ACAC at point EE. Prove that the circle (BKE)(BKE) is tangent to cc.
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