mrkya (basic check) geometrical property of circle

Find a, and state the reason.

• 2 x 55^o = 110^o

  (angle at centre = 2x angle at circumference)

• 180^o - 125^o = 55^o

  (angle in opposite segment)

• 55^o

  (angle in same segment)

• 180^o - 55^o = 125^o

  (exterior angle of quadrilateral)

State the geometrical property on why PQ is the diameter.

• perpendicular bisector of chord

• tangent perpendicular radius

• right angle in semicircle

• Pythagoras theorem

Find a, and state the reason.

• 51^o

  (corresponding angle)

• 87^o

  (angle sum of triangle)

• 46.5^o

  (base angle of isosceles triangle)

• 51^o

  (angle in same segment)

Angle PSQ is 46^o.

Find a, and state the reason.

• 83^o

  (angle in opposite segment)

• 88^o

  (interior angle, PS//QR)

• 90^o

  (right angle in semicircle)

• 97^o

  (opposite angle of cyclic quadrilateral)

PR is tangent to the circle at point Q.

State the geometrical property why QS is the diameter.

• tangent perpendicular radius

• perpendicular bisector of chord

• right angle in semicircle

• equal chords of circle

Find angle BCD, and state the reason.

• 40^o

  (angle sum of triangle)

• 70^o

  (angle in same segment)

• 70^o

  (equilateral triangle)

• 70^o

  (tangents from same external point)

State the geometrical property on why angle OMB = 90^o.

• perpendicular bisector of chord

• equal chords of circle

• tangent perpendicular radius

• Pythagoras theorem

Chords AB and PQ are each of length 18 units.

Find OK, and state the reason.

• 18 units

  (OA=OB=radius,

  base angle of isosceles triangle)

• 12 units

  (equal chords of circle)

• 12 units

  (OK is radius,

  base angle of isosceles triangle)

• 12 units

  (perpendicular bisector of chord)

Find a, and state the reason.

• 68^o

  (angle in opposite segment)

• 292^o

  (angle in opposite segment,

  reflex angle)

• 224^o

  (angle at centre = 2x angle at circumference)

• 238^o

  (exterior angle of cyclic quadrilateral)

Find angle AOB. State the reason.

• 104^o

  (angle at centre = 2x angle at circumference)

• 38^o

  (angle sum of right-angle triangle)

• 76^o

  (angle sum of isosceles triangle)

• 128^o

  (angle in opposite segment)