+0  
 
0
46
1
avatar

Triangle ABC, inscribed in a circle, has AB = 15 and BC = 35. A tangent to the circle is drawn at B, and a line through A parallel to this tangent intersects BC at D. Find DC. 

 

 Nov 3, 2020
 #1
avatar+452 
+3

Triangle ABC, inscribed in a circle, has AB = 15 and BC = 35. A tangent to the circle is drawn at B, and a line through A parallel to this tangent intersects BC at D. Find DC. 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hello, Guest! I think that BC should be 25 instead of 35. If BC = 25 then DC = 16

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let angle ABC = 90º

 

Angle BAD = arctan(15 / 35)

 

BD = tan∠BAD * AB = 6.428571429

 

DC = BC - BD = 28.57142857

 

 Nov 3, 2020

25 Online Users

avatar
avatar
avatar