symmetric properties of circles

Question 1

OM perpendicular to AB therefore, AM = MB

Answer 1

perpendicular bisector of chord

Question 2

AB = PQ, OM = ON

Answer 2

equal chords

Question 3

PQ perpendicular to OA, where PQ is a tangent to circle at A

Answer 3

tangent is perpendicular to radius

Question 4

PA = PB, where PA and PB are tangents to circle at A and B respectively and APO = BPO

Answer 4

tangents from an external point are equal

Question 5

AOB = 2 APB (rmb that it must touch the circumference)

Answer 5

angle at centre = 2 angle at circumference

Question 6

APB = 90 (rmb that it must touch the circumference)

Answer 6

right angle in a semicircle

Question 7

APB = AQB = ARB (rmb that it must touch the circumference)

Answer 7

angles in the same segment are equal

Question 8

a=c, b=d (rmb that it must touch the circumference)

Answer 8

angles in opposite segments are supplementary