Question

1. which arc is intercepted by ∠a in quadrilateral abcd inscribed in a circle? a. arc bcd b. arc ab c. arc ad d. arc bc 8. what is the slope of a line perpendicular to another line with a slope of 2? a. -2 b. 3 c. 1/2 d. -1/2 9. what is the property of the arcs that are drawn from two points on the angles sides when constructing an angle bisector? a. they must intersect b. they must be equal in length c. they must be parallel d. they must be perpendicular

Explanation:

Step1: Recall inscribed - angle property

An inscribed angle in a circle is an angle whose vertex is on the circle and whose sides contain chords of the circle. The arc intercepted by an inscribed angle is the arc that lies in the interior of the inscribed angle and has endpoints on the sides of the inscribed angle. For $\angle A$ in cyclic quadrilateral $ABCD$, the arc intercepted is $\overset{\frown}{BCD}$.

Step2: Recall perpendicular - slope relationship

If two lines with slopes $m_1$ and $m_2$ are perpendicular, then $m_1\times m_2=- 1$. Given $m_1 = 2$, then $m_2=-\frac{1}{2}$ since $2\times m_2=-1$.

Step3: Recall angle - bisector construction

When constructing an angle bisector, arcs are drawn from two points on the angle's sides with the same radius. These arcs must intersect to find a point that helps in drawing the angle - bisector.

Answer:

1. a. Arc $BCD$
2. d. $-\frac{1}{2}$
3. a. They must intersect