MathDB

9

Part of 1980 Austrian-Polish Competition

Problems(1)

equal segments wanted, tangents form endpoints of a diameter related

Source: Austrian-Polish 1980

5/25/2019
Through the endpoints AA and BB of a diameter ABAB of a given circle, the tangents ℓ\ell and mm have been drawn. Let C≠AC\ne A be a point on ℓ\ell and let q1,q2q_1,q_2 be two rays from CC. Ray qiq_i cuts the circle in DiD_i and EiE_i with DiD_i between CC and Ei,i=1,2E_i, i = 1,2. Rays AD1,AD2,AE1,AE2AD_1,AD_2,AE_1,AE_2 meet mm in the respective points M1,M2,N1,N2M_1,M_2,N_1,N_2. Prove that M1M2=N1N2M_1M_2 = N_1N_2.
geometryequal segmentsTangentscircle