100 points+! math

a diameter of a circle has endpoints p(-10, -2) and q(4,6)

a. find the center of the circle.
b. find the radius. if your answer is not an integer, express it in radical form.
c. write an equation for the circle.

if your answer is incorrect/incomplete or you are just answering for the points, your answer will be reported and removed and the points will get refunded.

P and Q are endpoints, so the center of the circle would be the midway point.

A. The midpoint is found using:

(x1 + x2 /2 , y1 +y2 /2)

-10 + 4 = -6 /2 = -3

-2 + 6 = 4 /2 = 2

The center of the circle is at (-3,2)

B) The radius would be the distance from the midpoint to an end point.

Using the distance formula:

√((x2-x1)^2 + (y2-y1)^2)

√(4 - -3^2 + 6-2^2)

√(7^2 + 4^2)

√(49+16)

√65

C) Using the circle equation form of (x-h)^2 + (y-k)^2 = r^2

H,K is the center point found in part A and r is the radius found in part B.

The equation becomes (x-(-3))^2 + (y -2)^2 = √65^2

Which simplifies to: (x+3)^2 + (y-2)^2 = 65

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

step-by-step explanation:

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