Question

Assume lines that look tangent, are tangent.Find the value of x.(The ones that are crossed out don’t need answered)

Answer 1

Take into account that for secant and tangent lines related to circles, use the following formula:

x = 1/2·(larger arc - smaller arc)

Then, you have, for the first circle:

larger arc = 360° - 124° = 236°

smaller arc = 124°

x = 1/2·(236° - 124°)

x = 1/2·(112°)

x = 56°

For the second circle, the value of x is the same that the given arc:

x = 124°

For the fourth circle:

larger arc = 171°

smaler arc = 67°

x = 1/2·(171° - 67°)

x = 1/2·(104°)

x = 52°

For the fifth circle:

x = 1/2·(101° + 39°)

x = 70°