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Work out the size of angle AOD.

 

 Apr 12, 2020
 #1
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If AD is tangent to the circle, then it is perpendicular to the radius OA.

Therefore, angle(DAO) = 90o.

Since there are 180o in the triangle, angle(AOD)  =  180o - 90o - 28o  =  62o

 

Since angle(AOD) is a central angle, it has the same number of degrees as the arc it cuts off.

This means that arc(AC) has 62o.

 

Angle(ABC) is an inscribed angle; therefore, it has one-half of the arc that it cuts off.

Angle(ABC) = 31o.

 Apr 12, 2020
 #2
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a)\(\angle\)OAD=90° because DA is a tangent to the circle

so, \(\angle\)AOD=62°

 

b)since \(\angle\)AOD=62°, minor arc CA has length 62°, and since \(\angle\)ABC is an inscribed angle in the circle, \(\angle\)ABC is half the measure of minor arc CA, so the answer is 31°

 Apr 12, 2020

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