Question

unit 1 – lesson 2 exit ticket: in the diagram shown, circles with centers at points a and b intersect at points c and d. segments (overline{ac}), (overline{bc}), (overline{ad}), and (overline{bd}) have been drawn to form quadrilateral acbd. circle a has a radius of length 5 cm and circle b has a radius of 3 cm. what is the perimeter of acbd? justify.

Explanation:

Step1: Identify radii lengths

In circle \( A \), radii \( \overline{AC} \) and \( \overline{AD} \) have length equal to the radius of circle \( A \), so \( AC = AD = 5 \, \text{cm} \). In circle \( B \), radii \( \overline{BC} \) and \( \overline{BD} \) have length equal to the radius of circle \( B \), so \( BC = BD = 3 \, \text{cm} \).

Step2: Calculate perimeter of quadrilateral \( ACBD \)

The perimeter \( P \) of a quadrilateral is the sum of its four sides. For \( ACBD \), the sides are \( AC \), \( BC \), \( BD \), and \( AD \). So, \( P = AC + BC + BD + AD \). Substituting the values: \( P = 5 + 3 + 3 + 5 \).

Step3: Simplify the sum

\( 5 + 3 + 3 + 5 = (5 + 5) + (3 + 3) = 10 + 6 = 16 \).

Answer:

The perimeter of quadrilateral \( ACBD \) is \( 16 \, \text{cm} \). This is because \( AC \) and \( AD \) are radii of circle \( A \) (each \( 5 \, \text{cm} \)) and \( BC \) and \( BD \) are radii of circle \( B \) (each \( 3 \, \text{cm} \)), so summing these four sides gives the perimeter.