TII-(72 24 x) {solved}

[Speed2001]

 

[Lokman Gökçe]

x = 72^o. I used similar approach at http://geomania.org/forum/fantezi-geometri/tii-(36-12-x)/msg7433/?topicseen#msg7433

Let's apply sine theorem at triangle ABC. Therefore BC = sin72/sin24 and AC = sin84/sin24.

We show that BC² = CD.AC. Hence line BC is tangent to circumcircle of triangle ABD. so x = m(CBD) = m(BAD) = 72^o.

Saludos