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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

5.15 Important Points in Circles

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

  • The line joining the centre of a circle to the mid point of a chord is perpendicular to the chord.

  • The perpendicular bisectors of two non-parallel chords of a circle intersect at the centre of the circle.

  • There is one and only circle passing through three non-collinear points in a plane.

  • If two chords of a circle are equal, they are equidistant from the centre.

  • The chords of a circle equidistant from the centre of the circle are equal.

  • Circles having the same radii are congruent.

  • In a circle (or congruent circles) equal arcs cut off equal chords.

  • In a circle if two chords are equal the arcs they cut off are equal.

  • The angles subtended by an arc of a circle at the centre is twice the angle it subtends at any point on the remaining circle.

  • Angles in the same segment are equal.

  • If A and B subtend equal angles at two points P, Q which are on the same side of AB then A, B, P, Q are concyclic.

  • The opposite angles of a cyclic quadrilateral are supplementary.

  • If the opposite angles of a quadrilateral are supplementary, then it is a cyclic quadrilateral.

  • If one side of a cyclic quadrilateral is produced the exterior angle formed is equal to the interior opposite angle.

  • If the exterior angle formed when one side of quadrilateral is produced is equal to the interior opposite angle, then it is a cyclic quadrilateral.

  • Equal chords (or arcs) of a circle make equal angles at the centre (of at the circumference).

  • The angle subtended by a minor arc is acute and the angle subtended by a major arc is obtuse.

  • The angle in the minor segment is obtuse and the angle in the major segment is acute. The angle in a semicircle is a right angle.

  • If two circles intersect, the line of centers is the perpendicular bisector of the common chord.

  • The perpendicular bisector of a chord bisects the arcs it contains.

  • A cyclic parallelogram is a rectangle. A cyclic rhombus is a square.

  • All regular polygons are cyclic.

  • An isosceles trapezium is cyclic. If a trapezium is cyclic then its non-parallel sides are equal.

  • The feet of the perpendiculars drawn to the sides of a triangle from a point on the circumcircle are collinear and the line is called Simon's Line or Pedal Line.

Directions: Choose the correct answer. Also write at least 10 examples of your own.
Q 1: All diameters of a circle are its chords.

Q 2: A chord of a circle is a subset of the circle.

Q 3: p is a rational number.

Q 4: An arc of a circle is a subset of the circle.

Q 5: A circle divides the plane in which it lies into three mutually disjoint sets of points.

Q 6: All chords of a circle are diameters.

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!

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