Question 1034621
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Given a circle in which the diameter AB equals 4cm. If two points C and D lie on the circle and the angle ABC= 18 degrees 
and angle BAD=36 degrees, find the length of the major arc CD.
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The answer and the situation depend on whether the points C and D lie in one side of the diameter AB or in different sides of AB.


1.  Let's assume that the points A and B lie in one side of the diameter AB.
    Let O be the center of the given circle.


<pre>
Since the measure of an inscribed angle in a circle is half the measure of the corresponding central angle, we have 

   the measure of the central angle AOC is equal to 2*18° = 36°, and 
   the measure of the central angle BOD is equal to 2*36° = 72°.

Thus the measure of the central angle COD is 180° - 36° - 72° = 72°, and 
   
    the measure of the major arc CD is 72°.
</pre>

2. &nbsp;If the points A and B lie in different sides of the diameter AB then

<pre>
   the measure of the major arc CD is 180° + 36° - 72° = 144°.
</pre>

<U>Answer</U>. &nbsp;&nbsp;Two answers: 72° and/or 144°.