Flashcards on Circle Theorems and Chords
Circle Theorems and Chords: Your Ultimate Guide & Examples
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Circle Geometry
18 cards
Card 1
Question: What is the relationship between a radius and a diameter of a circle?
Answer: The diameter is twice the radius (diameter = 2 × radius).
Card 2
Question: If MF is a diameter and MO and OF are radii, express MF in terms of MO.
Answer: MF = MO + OF and since MO = OF, MF = 2 × MO (MF = 2MO).
Card 3
Question: Given MO = ML + OL and OL = 3ML, write MO in terms of ML.
Answer: MO = ML + OL = ML + 3ML = 4ML.
Card 4
Question: Using MO = 4ML and MF = 2MO, express MF in terms of ML.
Answer: MF = 2(4ML) = 8ML.
Card 5
Question: If OP is the radius and MF is the diameter equal to 8ML, what is OP in terms of ML?
Answer: OP = (1/2)MF = (1/2)(8ML) = 4ML.
Card 6
Question: In a right triangle with sides expressed in ML: if OP = 4ML, OL = 3ML and LP = 7 cm, write the Pythagorean equation relating them.
Answer: (4ML)^2 = (3ML)^2 + 7^2 → 16·ML^2 = 9·ML^2 + 49.
Card 7
Question: Solve 16·ML^2 = 9·ML^2 + 49 for ML.
Answer: 7·ML^2 = 49 → ML^2 = 7 → ML = √7 cm.
Card 8
Question: State Theorem 1 used for a perpendicular from the centre to a chord.
Answer: A line from the centre perpendicular to a chord bisects the chord (it meets the chord at its midpoint).
Card 9
Question: Why is L the midpoint of chord QP when OL is perpendicular to QP?
Answer: Because a perpendicular from the centre to a chord bisects the chord, so OL ⟂ QP implies L is the midpoint of QP.
Card 10
Question: How can a right angle at the circumference be identified using a diameter?
Answer: An angle subtended by a diameter at the circumference is a right angle (90°).