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segment hm is the diameter of circle o.

secant ah intersects circle o at point t.

segment a f is tangent to circle o at point f.

fa = 21, at = 7, tm = 90, and th = x.

none of the angle measures are given.

1. solve for x. show your work.

2. what is the measure of angle h t m? explain how you know.

3. based on your answers to 1 and 2, what is the radius of circle o? show your work.

96

Step-by-step explanation:

IT IS CONVENTIONAL to let the letter s symbolize the length of an arc, which is called arc length. We say in geometry that an arc "subtends" an angle θ; literally, "stretches under."

Now the circumference of a circle is an arc length.  And the ratio of the circumference to the diameter is the basis of radian measure.  That ratio is the definition of π.

π   =  C

D.

Since D = 2r, then

π=C

2r

or,

C

r  =  2π.

arc lengthThat ratio -- 2π -- of the circumference of a circle to the radius, is called the radian measure of 1 revolution, which are four right angles at the center.  The circumference subtends those four right angles.

arc length

Radian measure of θ  =  s

r

Thus the radian measure is based on ratios -- numbers -- that are actually found in the circle.  The radian measure is a real number that indicates the ratio of a curved line to a straight, of an arc to the radius. For, the ratio of s to r does determine a unique central angle θ.

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)