Circle Properties
Muhtasari
Circles have a rich set of properties that appear across both Foundation and Higher papers. At Foundation level you need to know the standard terminology and the two key chord and tangent facts. At Higher level the circle theorems link angles, arcs, and cyclic quadrilaterals in ways that produce some of the most satisfying multi-step proofs on the paper.
This topic builds on your knowledge of angles and line properties. You will learn to name every part of a circle, prove chord and tangent relationships, and (at Higher) apply the full set of circle theorems including the alternate segment theorem and intersecting chord properties.
Malengo
- Recognise the terms 'centre', 'radius', 'chord', 'diameter', 'circumference', 'tangent', 'arc', 'sector' and 'segment' of a circle
- Understand chord and tangent properties of circles
- [Higher] Understand and use the internal and external intersecting chord properties
- [Higher] Recognise the term 'cyclic quadrilateral'
- [Higher] Understand and use angle properties of the circle including: angle subtended by an arc at the centre is twice the angle subtended at any point on the remaining part of the circumference; angle subtended at the circumference by a diameter is a right angle; angles in the same segment are equal; the sum of the opposite angles of a cyclic quadrilateral is 180 degrees; the alternate segment theorem
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Maelezo ya Somo
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Tathmini ya Somo
Hongera kwa kukamilisha somo la Circle Properties. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.
Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.
Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.
- The angle between a tangent and the radius at the point of contact is: A) 45 degrees B) 60 degrees C) 90 degrees D) 180 degrees Answer: C
- A chord is 24 cm long and the radius of the circle is 13 cm. What is the perpendicular distance from the centre to the chord? A) 5 cm B) 7 cm C) 10 cm D) 12 cm Answer: A
- The angle subtended by an arc at the centre of a circle is 140 degrees. What is the angle subtended at the circumference by the same arc? A) 35 degrees B) 70 degrees C) 140 degrees D) 280 degrees Answer: B
- ABCD is a cyclic quadrilateral. Angle A = 85 degrees. What is angle C? A) 85 degrees B) 95 degrees C) 105 degrees D) 180 degrees Answer: B
- Which of the following is the region between a chord and its arc? A) Sector B) Segment C) Semicircle D) Arc Answer: B
Fanyia kazi maswali haya kwenye programu
Fanyia kazi maswali haya kwenye programu
Vitabu Vinavyopendekezwa
Jifunze zaidi kutoka vyanzo huria
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Sehemu ya kitabu
Solve Geometry Applications: Circles and Irregular Figures
Use the properties of circles
"Prealgebra: Solve Geometry Applications: Circles and Irregular Figures" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/prealgebra/pages/9-5-solve-geometry-applications-circles-and-irregular-figures. Access for free at https://openstax.org/books/prealgebra/pages/1-introduction
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Fanya Mazoezi ya Maswali ya Majaribio
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