Asecant and a tangent to a circle intersect in a 42-degree angle. the two arcs of the circle intercepted by the secant and the tangent have measures in a 7: 3 ratio. find the measure of the third arc

The measure of the third arc is

Step-by-step  explanation:

step 1

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

in this problem

Let

x----> the greater arc of the circle intercepted by the secant and the tangent

y----> the smaller arc of the circle intercepted by the secant and the tangent

----> equation A

-----> equation B

Substitute equation B in equation A and solve for y

Find the value of x

step 2

Find the measure of the third arc

Let

z------> the measure of the third arc

we know that

-----> complete circle

substitute the values and solve for z

c

step-by-step explanation:

there is vertical asymptote at x = 2 and x = 0

vertical asymptote occurs at the points where the denominator is 0. so we can say that

x = 2 occurs when there is a factor (x-2) in the denominator, and

x = 0 occurs when there is a factor "x" in the denominator

thus, the denominator of the equation would have "x * (x-2)", this is option c only. that's the correct answer.

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