Circles — Flashcards
Madhya Pradesh Board · Class 9 · Mathematics
23 flashcards for Circles (Madhya Pradesh Board Class 9 Mathematics) to test yourself on key terms and facts. Sample: "What is the angle subtended by.
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What is the angle subtended by a chord at a point?
Answer
When a line segment (chord) PQ is drawn and a point R is taken not on the line containing PQ, then ∠PRQ formed by joining PR and QR is called the angle subtended by the line segment PQ at point R.
State the theorem about equal chords and angles at the center.
Answer
Theorem 9.1: Equal chords of a circle subtend equal angles at the centre. This means if two chords AB and CD are equal in length, then ∠AOB = ∠COD where O is the center.
What is the converse of the equal chords theorem?
Answer
Theorem 9.2: If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal. If ∠AOB = ∠COD, then chord AB = chord CD.
What happens when a perpendicular is drawn from the center to a chord?
Answer
Theorem 9.3: The perpendicular from the centre of a circle to a chord bisects the chord. If OM ⊥ AB where O is center and M is on chord AB, then AM = MB.
State the converse of the perpendicular bisector theorem.
Answer
Theorem 9.4: The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. If OM bisects chord AB, then OM ⊥ AB.
How is the distance of a line from a point defined?
Answer
The distance of a line from a point is defined as the length of the perpendicular drawn from the point to the line. This is the shortest distance between the point and the line.
What is the relationship between equal chords and their distances from the center?
Answer
Theorem 9.5: Equal chords of a circle (or of congruent circles) are equidistant from the centre. If chord AB = chord CD, then their perpendicular distances from center O are equal.
State the converse theorem about chords equidistant from center.
Answer
Theorem 9.6: Chords equidistant from the centre of a circle are equal in length. If two chords are at the same perpendicular distance from the center, then they are equal.
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