The two chords shown in the circle intercept the given arcs.
What is the measure of MPN?

Option (2)

Step-by-step explanation:

If two chords intersect inside the circle, measure of angle between them is half of the sum of intercepted arcs.

From the picture attached,

m∠MPN =

              =

              = 75°

Therefore, Option (2) will be the answer.

no not all of them.

step-by-step explanation:

some of them have a square base.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4