Question

applying angle relationships to find perimeter
what is the perimeter of kite obde?
12 units
22 units
38 units
58 units

Explanation:

Step1: Find length of AB (diameter)

First, use Pythagorean theorem on right triangle ABC:
$$AB = \sqrt{AC^2 + BC^2} = \sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26$$

Step2: Find length of OB (radius)

OB is half the diameter AB:
$$OB = \frac{AB}{2} = \frac{26}{2} = 13$$

Step3: Identify congruent sides of kite

In kite OBDE, $OB = OE = 13$, and $BD = DE = 6$.

Step4: Calculate perimeter

Sum all sides of the kite:
$$Perimeter = OB + OE + BD + DE = 13 + 13 + 6 + 6$$

Answer:

38 units