An acute [MATH]\triangle ABC[/MATH], inscribed in a circle [MATH]k[/MATH] with radii [MATH]R[/MATH], is given. Point [MATH]H[/MATH] is the orthocenter of [MATH]\triangle ABC[/MATH] and [MATH]AH=R[/MATH]. Find [MATH]\angle BAC[/MATH]. (Answer: [MATH]60^\circ[/MATH])
[MATH]AD[/MATH] is diameter, thus [MATH]\angle ACD = \angle ABD = 90^\circ[/MATH]. Also [MATH]HBDC[/MATH] is parallelogram because [MATH]HC || BD, HB||CD[/MATH]. It seems useless and I don't know how to continue. Thank you in advance!
[MATH]AD[/MATH] is diameter, thus [MATH]\angle ACD = \angle ABD = 90^\circ[/MATH]. Also [MATH]HBDC[/MATH] is parallelogram because [MATH]HC || BD, HB||CD[/MATH]. It seems useless and I don't know how to continue. Thank you in advance!