Mathematics - 0580 CIE

Circle Theorems

Bayani Gaba-gaba

Circle theorems are a set of elegant rules about the angles and lines inside a circle. They look like magic at first, but each one is reliable and, used together, they let you find angles that would otherwise be impossible to reach.

In this lesson you will calculate angles using circle properties: the angle in a semicircle and the tangent-radius right angle at Core, plus (at Extended) the angle at the centre, angles in the same segment, cyclic quadrilaterals and the alternate segment theorem.

Manufura

  1. Calculate unknown angles and give explanations using the following geometrical properties of circles: angle in a semicircle = 90° angle between tangent and radius = 90°.
  2. Calculate unknown angles and give explanations using the following geometrical properties of circles: angle in a semicircle = 90° angle between tangent and radius = 90° angle at the centre is twice the angle at the circumference angles in the same segment are equal opposite angles of a cyclic quadrilateral sum to 180° (supplementary) alternate segment theorem. (Extended only)

Takardar Darasi

Circle theorems combine angle reasoning with the special structure of a circle. They are a favourite exam topic because they reward clear, step-by-step reasoning.

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Nazarin Darasi

Barka da kammala darasi akan Circle Theorems. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

  1. The angle in a semicircle is: A. 45° B. 60° C. 90° D. 180° Answer: C
  2. The angle between a tangent and a radius is: A. 0° B. 45° C. 90° D. 180° Answer: C
  3. An angle at the centre is 100°. The angle at the circumference on the same arc is: A. 50° B. 100° C. 180° D. 200° Answer: A
  4. Opposite angles of a cyclic quadrilateral add up to: A. 90° B. 180° C. 270° D. 360° Answer: B
  5. One angle of a cyclic quadrilateral is 85°. Its opposite angle is: A. 85° B. 95° C. 105° D. 275° Answer: B

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Akwai a cikin manhajar Green Bridge

Zazzage manhajar Green Bridge CBT a wayar ka ko kwamfyuta ka don samun cikakkiyar bayanan darasi, tambayoyin aiki, da ƙari.

Cikakkiyar bayanan darasi tare da zane-zane
Mataimakiyar koyo da AI
Yi karatu ba tare da intanet ba, a kowane lokaci, a ko'ina
Akwai a Android, Windows, macOS, da Linux

Yi Aikin Tambayoyin Gwaji

Kana son yin aikin tambayoyin gwaji kan Circle Theorems? Sauke manhajar Green Bridge CBT don samun tambayoyin gwaji da cikakkun jarrabawa akan wannan batu.

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