CIRCLE THEOREMS REASONS

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I T Y R Q C A X H L Q E G R Q E G Y V A T
U A A S Q Y V I H K K W U A P L C Q P V D
I N G X H C M E J S Q T S L O C K N I M B
K G H R K L J P A J O G X T B R I H E C Q
I E W Y U I S D H K L P C E N I W G R B V
N N L V B C Q Y D K M H I R K C L E T O U
K T J O G Q C V I O T L M N X I V J N U L
O S D T N U U V E D N A J A K M J Q E Y Y
R T E U E A G G H E X H E T X E S S C T R
M O V W V D L F V M I X U E L S D H E R R
I A X F D R T P H R A L O S S A A I H F U
F C F V H I N R M Y L B A E Q N H T T V Q
E I K T Y L R M C V A D O G I I P F T W D
O R X B B A Q N S X D N I M Y S C J A V X
K C B B K T S V Y C P N C E E E H O E K F
F L N Q X E G H Y U W L H N Y L Q Q L L K
R E I F P R U L N X G S A T I G B M G I H
L G G X N A V L G Y S B V E C N M S N M S
C X M E Q L W Q L M A O N Y Q A G S A E Y
D F F L W S O S I C J F O Y H W H V C J A
E D F X F I D R L V X D D Q M P Q U V L K

Clues

  • A quadrilateral whose 4 vertices lie on the circumference of a circle is called a cyclic quadrilateral. Opposite angles of a cyclic quadrilateral add up to 180 degrees. (6, 13)
  • A tangent to a circle is always perpendicular to a radius at the point of contact (90 degree angle). Two tangents drawn from the same point are equal in length. (8, 2, 1, 6)
  • Angles at the circumference standing on a diameter are equal to 90 degrees (6, 2, 1, 4, 6)
  • The angle at the centre is twice the angle at the circumference ( standing on the same chord) (5, 2, 3, 6)
  • The angle between a tangent and a chord is equal to any angle made by that chord in the alternate segment. (9, 7)

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