Question

1. Given the following diagram. (a) Name the minor arc __________ Name the major arc ___________ (b) If the minor arc is 112°, what is the measure of the rest of the circle arc length? _____________ (c) Which line is the tangent? ___________ Which line is the secant? __________ (d) If XY is 11 and UX is 9, what is the length of UV? Show all work or no credit.

Answer 1

a) XY , XVY

b) 248°

c) UV , UY

d) 6√5 = 13.42

Explanation:

a) The minor arc is XY

The major arc is XVY

b) ∵ The measure of the minor arc is 112°

∵ The measure of the circle is 360°

∴ The measure of the rest arc = 360 - 112 = 248°

c) UV is the tangent to the circle

UY is the secant to the circle

d) ∵ UV is a tangent to the circle at V

∵ UY is a secant to the circle

∴ (UV)² = (UX) × (UY)

∵ UX = 9 and XY = 11 ⇒ ∴ UY = 11 + 9 = 20

∴ (UV)² = 9 × 20 = 180

∴ UV = √180 = 6√5 = 13.42