Question
A secant and a tangent to a circle intersect in a 42 degree angle. The two arcs of the circle intercepted by the secant and tangent have measures in a 7:3 ratio. Find the measure of the third arc.
If someone could help me figure out how to do the equations, then that would be great. Thank you.
If someone could help me figure out how to do the equations, then that would be great. Thank you.
Answers
42° = 1/2 (large-small)
so, large-small=84°
but, large = 7/3 * small
7/3 * small = small+84
4/3 * small = 84
small = 63
large = 147
So, since the three arcs add up to 360°,
63+147+x = 360
x = 150°
A nice discussion of the topic is found at
http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php
so, large-small=84°
but, large = 7/3 * small
7/3 * small = small+84
4/3 * small = 84
small = 63
large = 147
So, since the three arcs add up to 360°,
63+147+x = 360
x = 150°
A nice discussion of the topic is found at
http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php
given ab is a tangent of point x, ab=70 and xd= 12 what is the measure of db?
amosc @ unique4418
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