+0  
 
0
57
1
avatar

In the given figure ABCD is a cyclic quadrilateral.The tangent to the circle at B meets DC produced at F.  If $\angle EAB=85°$ and $\angle BFC=50°$ , find $\angle CAB$.

 

 Jan 25, 2021
 #1
avatar+116126 
+1

Angle DAC   = 180    - 85  =   95° 

 

And since ABCD  is a cyclic quadtilateral, then angle   DCB =  180  -95  =  85°

 

Then angle BCF  =180   -  85  = 95°

 

So angle FBC   =180  - 50  -95   = 35°

 

And this  =  (1/2)  measure of  minor arc BC    =   2 (35)    =  70°

 

But angle CAB    is an inscribed angle itercepting this arc....so its measure = (1/2) (70) =  35°

 

 

cool cool cool

 Jan 25, 2021

59 Online Users

avatar
avatar
avatar
avatar
avatar