Circle parts and geometric definitions · Higher
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| segment/ˈseɡmənt/ | 弓形 | gōng xíng |
A round window can be split by a straight chord or by two radii. These cuts create different regions, even though both use a curved boundary.
- A round window can be split by a straight chord or by two radii. These cuts create different regions, even though both use a curved boundary.
- This lesson studies segment 弓形: A region bounded by a chord and its corresponding arc.
Choose the mathematical structure
- A circle consists of points a fixed radius from its centre. A diameter is a chord through the centre and has length 2r. A chord joins two circumference points; an arc is part of the circumference. A sector lies between two radii and an arc. A segment lies between a chord and an arc. A tangent touches at one point and is perpendicular to the radius there.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines segment?
A region bounded by a chord and its corresponding arc.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
For centre O and radius 5 cm, every circumference point is 5 cm from O and the diameter is 10 cm. A chord 3 cm from O has half-length √(5²-3²)=4 cm, so its whole length is 8 cm. The perpendicular from O meets the chord at its midpoint. Joining the two chord endpoints to O creates a sector; the smaller region between chord and arc is a segment. At the rightmost circumference point, the vertical touching line is tangent and the horizontal radius is perpendicular to it. The circumference is a length, 2πr=10π cm, rather than an area.
Circle parts and geometric definitions
A circle consists of points a fixed radius from its centre
Classify the worked-case statements, then explain the units or invariant that justifies each decision.
Find the diameter when radius is 5 cm.
Diameter=2×5=10 cm.
Test a tempting shortcut
- A chord need not pass through the centre; only a diameter must. Sector and segment have different straight boundaries. Do not confuse circumference length with the shaded area inside a circle.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
A sector is bounded by a chord and an arc. This claim is false. Explain which definition or assumption it violates.
Find the half-chord for radius 5 and perpendicular centre distance 3.
Use √(25-9)=4 cm.
A sector is bounded by a chord and an arc.
A chord need not pass through the centre; only a diameter must. Sector and segment have different straight boundaries. Do not confuse circumference length with the shaded area inside a circle.
Interpret a new situation
- AQA G9 includes all named circle parts at Foundation. Use the given radius and position labels to identify the part; Higher circle-theorem proofs are developed separately.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Find the whole chord length in that example.
The perpendicular bisects the chord: 2×4=8 cm.
Match each part of a complete solution to its purpose.
An assumption justifies the model; a check tests the result; interpretation connects it to the question.
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A region bounded by a chord and its corresponding arc. Choose the relationship, show the method, check its assumptions and interpret the result.