Circle theorems

Question 1

1

Answer 1

the angle in a semicircle is a right angle

Question 2

2

Answer 2

the angle between a tangent and its radius at the point of tangency is a right angle

Question 3

3

Answer 3

a triangle formed by 2 radii is isosceles

Question 4

4

Answer 4

the perpendicular bisector of a chord always passes through the centre of the circle

Question 5

5

Answer 5

angles at the centre are double that at the circumference of the same arc

Question 6

6

Answer 6

angles subtended by the ends of a chord in the same segment are equal

Question 7

7

Answer 7

opposite angles in a cyclic quadrilateral sum to 180 degrees

Question 8

8

Answer 8

2 non-parallel tangents always meet at a point and are equal in length, creating 2 congruent right-angled triangles

Question 9

9

Answer 9

-alternate segment theorem

-the angle between a tangent and a chord is equal to the angle subtended from the ends of the chord in the alternate segment

Question 10

10

Answer 10

for two chords AB and CD that meet at point P, ab = cd

intersecting chord theorem