Points X and Y are on a circle centered at O, and point Q is outside the circle such that line QX and line QY are tangent to the circle. If angle XQO = 32, then what is the measure of minor arc XY, in degrees?

Guest Jan 15, 2020

#3**+1 **

See the following image

Note that OXQY forms a quadrilateral

Since QX and QY are tangent to the circle, then angles QXO and QYO = 90 °

And by symmetry, angle XQY = 2(32) = 64°

And the interior angles of a quadrilateral sum to 360°

So

QXO + QYO + XQY + XOY = 360

90 + 90 + 64 + XOY = 360

244 + XQY = 360 subtract 244 from both sides

XOY = 116°

And since XOY is a central angle........then minor arc XY has the same measure = 116°

CPhill Jan 15, 2020