Circles

Question 1

Theorem 1

Answer 1

Equal chords of a circle subtend equal angles at the centre

Question 2

Theorem 2

Answer 2

If the angles subtended by two chords at the centre are equal,then the chords are equal

Question 3

Theorem 3

Answer 3

The perpendicular drawn from the centre of a circle to the chord bisects the chord

Question 4

Theorem 4

Answer 4

The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord

Question 5

theorem 5

Answer 5

equal chords of a circle are equidistant from the centre (for congruent circles as well)

Question 6

theorem 6

Answer 6

chords equidistant from the centre are equal in length

Question 7

theorem 7

Answer 7

if two chords are equal, then their corresponding arcs are equal

Question 8

theorem 8

Answer 8

the angle subtended by an arc at the centre is double the angle subtended by it at any other remaining part of the circle.

Question 9

theorem 9

Answer 9

angles in the same segment are equal

Question 10

theorem 10

Answer 10

angles in a semicircle is a right angle

Question 11

theorem 11

Answer 11

the sum of either pair of opposite angles in a cyclic quadrilateral is 180 degrees.

Question 12

theorem 12

Answer 12

if the sum of a pair of opposite angles of a quadrilateral is 180 degrees, then the quadrilateral is cyclic