company logo
a company has two options for logos as shown. the radius of each logo is 1 foot.
jayson wants to find out specific measurements from each logo.
jayson notices in logo a that $ \overline { a b } $ and $ \overline { c d } $ are located outside of the circle and points $ b $ and $ c $ are points of
which statement is true?
a. $ \overline { a b } $ is not perpendicular to $ \overline { o b } $ and $ \overline { d c } $ is not perpendicular to $ \overline { o c } $ because points $ b $ and $ c $ are the
endpoints of a secant of the circle.
b. $ \overline { a b } $ is perpendicular to $ \overline { o b } $ and $ \overline { d c } $ is perpendicular to $ \overline { o c } $ because points $ b $ and $ c $ are the
endpoints of a secant of the circle.
c. $ \overline { a b } $ is not perpendicular to $ \overline { o b } $ and $ \overline { d c } $ is not perpendicular to $ \overline { o c } $ because points $ b $ and $ c $ are the
endpoints of the radius of the circle.
d. $ \overline { a b } $ is perpendicular to $ \overline { o b } $ and $ \overline { d c } $ is perpendicular to $ \overline { o c } $ because points $ b $ and $ c $ are the
endpoints of the radius of the circle.

Question

Accepted Answer

# Explanation:
## Step1: Recall the property of tangent
A tangent to a circle is perpendicular to the radius at the point of tangency. In Logo A, $\overline{AB}$ and $\overline{DC}$ are tangents. For $\overline{AB}$, the radius is $\overline{OB}$ (since $B$ is the point of tangency). For $\overline{DC}$, the radius is $\overline{OC}$ (since $C$ is the point of tangency). So $\overline{AB}\perp\overline{OB}$ and $\overline{DC}\perp\overline{OC}$. Also, $B$ and $C$ are points on the circle, not endpoints of the radius.
## Step2: Analyze each option
- Option A: $\overline{AB}$ is a tangent (so $\overline{AB}\perp\overline{OB}$), not “$\overline{AB}$ is not perpendicular to $\overline{OB}$”
- Option B: $\overline{AB}$ is a tangent (so $\overline{AB}\perp\overline{OB}$), not “$\overline{AB}$ is perpendicular to $\overline{OB}$ and endpoints of a secant”
- Option C: $\overline{AB}$ is a tangent ($\overline{AB}\perp\overline{OB}$), $\overline{DC}$ is a tangent ($\overline{DC}\perp\overline{OC}$), $B$ and $C$ are points on the circle (not endpoints of the radius)
- Option D: $B$ and $C$ are points on the circle (not endpoints of the radius)

# Answer:
C. $\overline{AB}$ is not perpendicular to $\overline{OB}$ and $\overline{DC}$ is not perpendicular to $\overline{OC}$ because points $B$ and $C$ are the endpoints of the radius of the circle.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the property of tangent

Step2: Analyze each option

Answer: