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Questions and Answers
In the first activity, if the diameter of the circle is 20 cm and DE = 16 cm, what is the length of CF?
In the first activity, if the diameter of the circle is 20 cm and DE = 16 cm, what is the length of CF?
In the second activity, if QR = 24 and OP = 10, what is the radius of the circle?
In the second activity, if QR = 24 and OP = 10, what is the radius of the circle?
In the third activity, which theorem states that congruent chords of a circle are equidistant from the center?
In the third activity, which theorem states that congruent chords of a circle are equidistant from the center?
For testing congruence in the example of Activity III, which test of congruence of triangles will be useful?
For testing congruence in the example of Activity III, which test of congruence of triangles will be useful?
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In figure 3.99, if MO = 25 and ML = 9, what is the length of segment ON?
In figure 3.99, if MO = 25 and ML = 9, what is the length of segment ON?
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In figure 3.101, if segment SQ is parallel to segment RP, what is the relationship between angles ∠MRS and ∠NRP?
In figure 3.101, if segment SQ is parallel to segment RP, what is the relationship between angles ∠MRS and ∠NRP?
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In figure 3.100, what is the relationship between angles ∠PRQ and ∠PSQ?
In figure 3.100, what is the relationship between angles ∠PRQ and ∠PSQ?
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In figure 3.102, if points A, B, C, D form a cyclic quadrilateral, what can be concluded about the angles of this quadrilateral?
In figure 3.102, if points A, B, C, D form a cyclic quadrilateral, what can be concluded about the angles of this quadrilateral?
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What is the total angle when the measures of ∠ADB and ∠AEB are added together?
What is the total angle when the measures of ∠ADB and ∠AEB are added together?
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What is the relationship between the angles ∠ACB and ∠ADB based on the activity described?
What is the relationship between the angles ∠ACB and ∠ADB based on the activity described?
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What can be said about the angles ∠AHB, ∠ADB, ∠AFB, and ∠AGB based on the activity?
What can be said about the angles ∠AHB, ∠ADB, ∠AFB, and ∠AGB based on the activity?
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What is the relationship between the measures of ∠AEB and ∠AIB from the activity?
What is the relationship between the measures of ∠AEB and ∠AIB from the activity?
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Study Notes
Circle Theorems
- In a circle, if the diameter is 20 cm and the length of a chord (DE) is 16 cm, the length of CF can be calculated.
- If QR = 24 and OP = 10, the radius of the circle can be determined.
- The theorem that states congruent chords of a circle are equidistant from the center is the Congruent Chords Theorem.
Congruence of Triangles
- To test congruence in the example of Activity III, the SAS (Side-Angle-Side) test of congruence of triangles is useful.
Properties of Circles
- In a circle, if MO = 25 and ML = 9, the length of segment ON can be calculated.
- If segment SQ is parallel to segment RP, angles ∠MRS and ∠NRP are equal.
- Angles ∠PRQ and ∠PSQ are supplementary.
- In a cyclic quadrilateral, the sum of opposite angles is 180°.
Angle Relationships
- The total angle when the measures of ∠ADB and ∠AEB are added together is 180°.
- Angles ∠ACB and ∠ADB are equal.
- Angles ∠AHB, ∠ADB, ∠AFB, and ∠AGB are equal.
- The measures of ∠AEB and ∠AIB are equal.
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Description
Review the properties of chords in circles and apply them to solve a problem involving a chord DE of length 16 cm in a circle with diameter 20 cm. Given that CF is perpendicular to DE, calculate the length of CF.
