1) Points A and B lie on a circle centered at O, and point P is outside the circle such that AP and BP are tangent to the circle. If angle APO = 26 degrees, then what is the measure of minor arc AB, in degrees?

2)Lines PTQ and PUR are tangent to a circle, as shown below. If angle QTA = 41 degrees and angle RUA = 63 degrees, then find angle QPR, in degrees.

Image -https://latex.artofproblemsolving.com/c/c/1/cc16b62c53fd72035896c4f0760d814431cc0883.png

3)In cyclic quadrilateral PQRS, \(\[\frac{\angle P}{2} = \frac{\angle Q}{3} = \frac{\angle R}{4}.\]\). Find the largest angle of quadrilateral PQRS, in degrees.

4) In rectangle EFGH, EH = 3 and EF = 4. Let M be the midpoint of EF, and let X be a point such that MH = MX and angle MHX = degrees. as shown below. Find angle XGH, in degrees.

Image~ https://latex.artofproblemsolving.com/7/e/9/7e94926930b2c8fb022fe9a340b8ee65178067a6.png

5)Two of the sides of a triangle are 11 and 17. The length of the third side is also a positive integer. How many different possible values are there for the third side length? (Assume that the triangle is non-degenerate.)

6)The distance from Capital City to Little Village is 140 miles. From Capital City to Mytown is 60 miles, from Mytown to Yourtown is 25 miles, and from Yourtown to Little Village is 55 miles. How far is it from Mytown to Little Village?

7)Triangle ABC has altitudes AD, BE, and CF. If AD = 12, BE = 14, and CF is a positive integer, then find the largest possible value of CF.

PLEASE HELP!!!!

Puplove Apr 8, 2020

#1**0 **

I'll just do the ones I know how to do quickly...

5) If the two sides are 11 and 17, the third side ,x, can be 6 21 values of the third side.

6) The Cities look like this...

---------------------------------------140 miles-----------------------------

Capital City----60 miles----Mytown----25 miles----Yourtown----55 miles----Little Village

This means that the distance from Mytown to Little Village is 25+55= **80 miles**.

Hope it helps!

HELPMEEEEEEEEEEEEE Apr 8, 2020