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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 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?
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?
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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?
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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?
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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?
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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?
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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.
