SOLUTION: EVOL is a cyclic quadrilateral, inscribed in a circle with center S. Given that the radius of this circle is 25 in. and angle VEL is 55 degrees. explain your work to find the follo

Let the center be K. Draw radii KV and KL [which are 25 in. each. We'll get
that in part d)].  Let's answer part b) first

Since inscribed angle VEL is 55°, then 55° is one-half the measure of
its intercepted arc.  So minor arc VL is twice 55°, or 110°.

Let's do part a) next

The measure of major arc VL = 360°-the measure of minor arc VL 
= 360-°110°=250° 

Let's do part c) next

Since inscribed angle VOL subtends major acc VL, which is 250°, then 250° is
one-half the measure of its intercepted arc. So angle VOL is 125°  

Since we found minor arc VL to have measure 110° in part a), Central angle
VKL also has measure 110°.

Now we will draw KP perpendicular to VL.  

 

Since triangle VKL is isosceles, KP bisects angle VKL, which is 110°, and
angle VKP is 55°.






Since chord VL is twice VP, chord VL has length 40.95760221,

Edwin