What is the value of a + b? You may assume that the ray is tangent to the circle.
2 answers:
See the attached picture to better understand the problem
we know that
if the <span>ray is tangent to the circle
</span>then
diameter ABC is perpendicular to ray FC
and
<span>the value of (a + b) is equal to 90 degrees
</span>let's check it<span>
step 1
find measure arc DC
arc DC=180-54-----> 126</span>°
∠DBC=126°------> by central angle
<span>
step 2
find angle a</span>°
we know that
<span>The inscribed angle measures half of the arc it comprises.
</span><span>so
</span>∠a=arc AD/2----> 54/2--->∠a= 27°
∠b=arc DC/2----> 126/2---> ∠b=63°
<span>
</span>∠a+∠b=27+63----> 90°------> is ok
<span>
the answer is
a+b is equal to 90 degrees
</span>
we know that
if the <span>ray is tangent to the circle
</span>then
diameter ABC is perpendicular to ray FC
and
<span>the value of (a + b) is equal to 90 degrees
</span>let's check it<span>
step 1
find measure arc DC
arc DC=180-54-----> 126</span>°
∠DBC=126°------> by central angle
<span>
step 2
find angle a</span>°
we know that
<span>The inscribed angle measures half of the arc it comprises.
</span><span>so
</span>∠a=arc AD/2----> 54/2--->∠a= 27°
∠b=arc DC/2----> 126/2---> ∠b=63°
<span>
</span>∠a+∠b=27+63----> 90°------> is ok
<span>
the answer is
a+b is equal to 90 degrees
</span>
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