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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.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer: i would say b

step-by-step explanation:

with the way the question is worded, i believe b is the answer

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