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.

Question

If someone could help me figure out how to do the equations, then that would be great. Thank you.

Answer 1

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

Answer 2

given ab is a tangent of point x, ab=70 and xd= 12 what is the measure of db?

Answer 3

amosc @ unique4418