161) Incircle and circumcircle. Find the radius of circumcircle | Math Olympiad | Geometry.

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[Okkk]

Applying Euler theorem of the distance d between the incenter r=2 and circumcenter R of the triangle is given by d=sqrt(R^2-2R*r) together with the result that the chord DC is bisected by the perpendicular line form the circumcenter point O. Therefore, we have the following equation:
(R^2-2*R*r)-(1/2)^2 +(11/2)^2=R^2
Solving for R we obtain R=15/2=7.5.

[じーちゃんねる-vn]

AngleACD=BCD=α AngleCBI=ABI=β AngleDIB=DBI=α+β ∴DB=6 sinα=2/5 sine rule 2R=6/(2/5)=15 ∴R=15/2

[solimana-soli]

Very difficult question!! Thanks for sharing