+0

# Geometry question

0
82
4

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?

Jan 15, 2020

#1
0

Arc XY is 142 degrees.

Jan 15, 2020
#2
0

I'm sorry, could you include a solution? I'd like to understand how to solve the problem on my own.

Guest Jan 15, 2020
#3
+109739
+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°

Jan 15, 2020
edited by CPhill  Jan 15, 2020
edited by CPhill  Jan 15, 2020
#4
+1

Thanks, I was actually able to solve it right before you lol!

Didn't properly understand the question so I didn't draw a proper diagram; once I did the solution was obvious.

Guest Jan 15, 2020