Mathematics - International - 0607 CIE

Circle Theorems II

Bayani Gaba-gaba

Beyond the angle theorems, circles have neat symmetry properties about their chords and tangents. These let you find lengths and prove that certain lines pass through the centre.

In this lesson you will use the property that tangents from an external point are equal in length (Core), and (at Extended) that equal chords are equidistant from the centre and the perpendicular bisector of a chord passes through the centre.

Manufura

  1. Use the symmetry property of circles that tangents from an external point are equal in length.
  2. Use the following symmetry properties of circles: equal chords are equidistant from the centre the perpendicular bisector of a chord passes through the centre tangents from an external point are equal in length. (Extended only)

Darasin Sauti

Saurari wannan darasi a cikin manhaja

Taswirar tunani

An zana wannan batu don ka ga yadda ra'ayoyi ke hadewa.

Bude taswirar tunani a cikin manhaja

Katunan tunawa

Gwaji mai sauri kan abin da ake jarraba a wannan batu.

Yi atisayen wadannan katuna a cikin manhaja

Takardar Darasi

These symmetry facts often unlock a length or right angle the angle theorems alone cannot, especially with tangents and chords.

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Nazarin Darasi

Barka da kammala darasi akan Circle Theorems II. Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, 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. Two tangents from an external point P are: A. perpendicular B. equal in length C. parallel D. always 90° Answer: B
  2. If one tangent PA = 7 cm from P, the other tangent PB is: A. 3.5 cm B. 7 cm C. 14 cm D. cannot tell Answer: B
  3. The perpendicular from the centre to a chord: A. bisects the chord B. is a tangent C. equals the radius D. is a diameter Answer: A
  4. The perpendicular bisector of a chord passes through: A. a tangent point B. the midpoint only C. the centre D. an external point Answer: C
  5. Equal chords in a circle are: A. parallel B. perpendicular C. equidistant from the centre D. diameters Answer: C

Yi aikin wadannan tambayoyi a cikin manhaja

Yi aikin wadannan tambayoyi a cikin manhaja

Yi Aikin Tambayoyin Gwaji

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

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