Asked by Ann

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.

Answers

Answered by Steve
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
Answered by john
given ab is a tangent of point x, ab=70 and xd= 12 what is the measure of db?
Answered by athena
amosc @ unique4418
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