Question

Circle P is shown. Tangents R S and T S intersect at point S outside of the circle to form angle x. The first arc formed is arc y, and the second arc formed is arc z. Which statement is true regarding the diagram of circle P? The sum of y and z must be 2x. The sum of y and z must be One-halfx. The difference of z and y must be 2x. The difference of z and y must be One-halfx.

Answer 1

" The difference of z and y must be 2x "

Explanation:

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Answer 2

The true statement is " The difference of z and y must be 2x " ⇒ 3rd

Explanation:

If two tangents to a circle intersected outside it, then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs.

∵ P is a circle

∵ RS and TS are to tangents to circle P

∵ The tangents RS and TS intersected at point S outside the circle

∵ They formed angle x between them

∴ x =
`(1)/(2)` (m major arc RT - m minor arc RT)

∵ The first arc formed is arc y

∴ The minor arc RT is y

∵ The second arc formed is arc z

∴ The major arc RT is z

∴ x =
`(1)/(2)` (z - y)

- Multiply both sides by 2

∴ 2 x = z - y

∴ The difference of z and y must be 2 x

The true statement is " The difference of z and y must be 2x "