Asked by logan
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.
All Answers 1
Answered by
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The difference of z and y must be 2x.
Reason: If y is the minor arc and z the major arc, z = 360° − y. The angle between the two tangents equals 1/2(z − y), so x = 1/2(z − y), hence z − y = 2x. Equivalently x = 180° − y, giving the same result.
Reason: If y is the minor arc and z the major arc, z = 360° − y. The angle between the two tangents equals 1/2(z − y), so x = 1/2(z − y), hence z − y = 2x. Equivalently x = 180° − y, giving the same result.
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