Circle Theorems And Constructions
Gbogbo ọrọ náà
A circle looks simple, but the angles hiding inside it obey a tight web of rules: an angle at the centre is always exactly twice its counterpart on the circumference, opposite corners of a cyclic quadrilateral are always supplementary, and a tangent meets its radius at a perfect right angle every time. This topic gives you the full set of Edexcel circle theorems, proved rather than just stated, plus the loci and constructions that turn these ideas into precise ruler-and-compasses drawings.
You will learn to identify which theorem a diagram is asking for, chase an angle through several steps of reasoning, and construct an angle bisector and a perpendicular bisector using nothing but a straight edge and compasses. Circle theorem questions reward students who can name the exact property they used, so this note treats every reason as seriously as the number attached to it.
Ebumnobi
- Understand and use chord, angle and tangent properties of circles
- Know and use properties of a cyclic quadrilateral, including intersecting chord properties and the alternate segment theorem
- Understand and use loci in two dimensions
- Construct bisector of an angle and perpendicular bisector of a straight line using ruler and compasses
Akọmọ Ojú-ẹkọ
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ayẹwo Ẹkọ
Ekele diri gi maka imecha ihe karịrị na Circle Theorems And Constructions. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- O is the centre of a circle. Points A and B lie on the circumference. The angle at the centre, angle AOB, is 94 degrees. What is the angle at the circumference, angle ACB, for a point C on the major arc? A) 47 degrees B) 94 degrees C) 188 degrees D) 43 degrees Answer: A
- ABCD is a cyclic quadrilateral with angle B = 78 degrees. What is angle D? A) 78 degrees B) 90 degrees C) 102 degrees D) 180 degrees Answer: C
- TA is a tangent to a circle at point A, and O is the centre. What is the size of angle OAT? A) 45 degrees B) 60 degrees C) 90 degrees D) It depends on the radius Answer: C
- Chords PQ and RS intersect inside a circle at point X, with PX = 4 cm, XQ = 9 cm and RX = 6 cm. What is XS? A) 5 cm B) 6 cm C) 7.5 cm D) 13.5 cm Answer: B
- Which locus describes the set of points equidistant from two fixed points P and Q? A) A circle centred at the midpoint of PQ B) The perpendicular bisector of PQ C) A line parallel to PQ D) The angle bisector at P Answer: B
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Àwọn Ìwé Tó Dáa Láti Kà
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Circle Theorems And Constructions? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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