Maths GCSE circle theoremsUsing angle facts, properties of triangles, straight lines, tangents and radii to solve problems in circles
Maths gcse circle theorems proofProving circle theorem that angle at centre equals twice angle at circumference
Maths GCSE circle theoremsUsing circle theorems about tangents to solve angles in triangles
Maths GCSE circle theorems and congruencyProving congruency with circle theorems
Right Hypotenuse Side (RHS)
Angle in semi circle gives right angle - 90 degrees (R)
Diameters are hypotenuse (H)
AD is common (S)
Maths gcse circle theoremsSolving angles in circles with a tangent
Maths GCSE circle theorems proofProof of angle at Centre is twice angle at circumference.
Key points: Construction, properties of radius (radii) and isosceles triangle and exterior angle.
Video was rushed trying to get done before bell rang so construction wasn’t quite straight line and initially mislabelled angle y, but can retake.
Also camera didn’t show final line of proof:
BAC = x + y
BOC = 2x + 2y = 2(x + y)
Hence angle at Centre is twice angle at circumference
Will get better! Thanks for watching!
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Maths Circle Theorems Angle in semi circleChalk drawing of angle in semi circle is a right angle
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Proof includes Pythagoras or congruency for two triangles in a kite.
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Use of radii, isosceles triangles and exterior angle to prove.
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Have a look at circle theorems playlist of other videos