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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.

 

 

Please help and explain ASAP, thank you!!!

 Jul 31, 2020
 #1
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k works out to 4/11.

 Jul 31, 2020
 #2
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Sorry about the terrible presentation,

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

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