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In the figure, the line $BD$ is tangent to the circle at $C$. The line $AD$ passes through the centre $O$ of the circle and intersects the circle at $E$.

It is given that $\angle CDE=34^{\circ}$ and $\angle DCE=x^{\circ}$.

Find the value of $x$.

 

 Jan 27, 2021
 #1
avatar+1371 
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I really have no idea on how to solve this, but I have a feeling it's 26. 

Triangle EOC looks like a equilateral triangle which would make DEC 120. 

180 - 120 - 34 = 26. 

 

Sorry I wasn't able to help more. 

 

=^._.^=

 Jan 27, 2021
 #2
avatar+118665 
+1

Connect OC

And a radius  meeting a tangent forms a 90°   angle

 

So in triangle   OCD     angle   DOC  = 180 -90  -34  = 56°

 

And this equals the measure  of  minor arc EC

 

And  by the tangent-chord theorem,  angle DCE  =(1/2)  the measure  of this arc  =(1/2)(56)  = 28°

 

 

cool cool cool

 Jan 27, 2021

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