+0

+2
70
2
+157

An acute isosceles triangle, ABC, is inscribed in a circle. Through B and C, tangents to the circle are drawn, meeting at point D. If $$\angle ABC = \angle ACB = 2 \angle D$$ and $$\angle BAC = k \pi$$ in radians, then find k.

Jul 31, 2020

#1
0

k works out to 4/11.

Jul 31, 2020
#2
+110817
+1

GeoGebra froze on me and I am not about to start all over, so i just took a pic.

Now check what i have done by drawing your own pic. I could have made a mistake,

Get a equation for the angle sum of kite XBDC

Get a equation for the angle sum of triangle ABC

Solve simultaneously to find solutions for  alpha and k.

Aug 1, 2020