MATH SOLVE

5 months ago

Q:
# 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.

Accepted Solution

A:

Answer:a) XY , XVYb) 248°c) UV , UYd) 6√5 = 13.42Step-by-step explanation:a) The minor arc is XY The major arc is XVYb) ∵ 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 circled) ∵ 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