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Vikki
20 days ago
5

Fill in the blank. Given O below, you can conclude that OD is congruent to ___________.

Mathematics
2 answers:
zzz [9K]20 days ago
6 0

We can deduce that \boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }. Option (A) is the correct choice.

Detailed Explanation:

Provided:

The options are listed below,

A. \overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}}.

B. \overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{EF}}}.

C. \overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{AB}}}.

D. \overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OC}}}.

Clarification:

The lengths of AB and EF are 9.07{\text{ units}}.

AB and EF are chords of the circle that are of equal length.

OD and OB serve as the perpendicular bisectors of chords AB and EF.

The mentioned chords are equidistant from the center of the circle.

We can conclude that \boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }. Option (A) is the correct answer.

To Explore Further:

  1. What would be the loss incurred by a clothing manufacturer who purchased 500 m2 of this fabric, priced at $1.00/yard if 0.9144m equals 1 yard? .
  2. In a reference book, if the ocean's total volume is found to be 1.4×109km3, how can you find the mass utilizing the water's density included within, and first convert that volume to cubic meters? .

Response Information:

Grade: High School

Subject: Mathematics

Chapter: Lines and Rays

Tags: congruent, fill, blank, conclude, OH, OE, chord, tangent, displacement, two chords, radius, center, circle, equidistant,

Inessa [9K]20 days ago
4 0

In a circle centered at O, there are two chords, AC and EF, both measuring 9.07.

OD and OB are the perpendiculars from the center O to the chords AC and EF, indicating their distance from the center.

The theorem concerning circles states that chords of equal length are equidistant from the center.

This means that OD and OB are equal.

Thus, the correct answer is Option A.

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