Gr 11 Math Ch 8: Circle Geometry
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Questions and Answers

What is the angle between a tangent to a circle and a chord drawn from the point of contact?

  • Twice the angle subtended by the chord in the alternate segment
  • Equal to the angle subtended by the chord in the alternate segment (correct)
  • Half of the angle subtended by the chord in the alternate segment
  • Complementary to the angle subtended by the chord in the alternate segment

    • What is the characteristic of two tangents drawn from the same point outside a circle?

  • They are unequal in length
  • They are perpendicular to each other
  • They intersect at the center of the circle
  • They are equal in length (correct)

    • What is the line segment joining the center of a circle and the midpoint of a chord?

  • Diameter of the circle
  • Tangent to the circle
  • Perpendicular to the chord (correct)
  • Parallel to the chord

    • What is the characteristic of a line segment from the center of a circle perpendicular to a chord?

    <p>It bisects the chord</p> Signup and view all the answers

    What is the relationship between the angle at the center of a circle and the angle on the circle subtended by the same chord or arc?

    <p>The angle at the center is twice the angle on the circle</p> Signup and view all the answers

    What is the relationship between angles on a circle that are subtended on the same side by the same arc?

    <p>They are equal</p> Signup and view all the answers

    What can be said about chords that subtend equal angles at the center of a circle?

    <p>They are equal in length</p> Signup and view all the answers

    What is the characteristic of a diameter of a circle?

    <p>It subtends right angles on the circle</p> Signup and view all the answers

    What is the term for a part of the circle that is cut off by a chord?

    <p>Segment</p> Signup and view all the answers

    What is the special chord that passes through the center of the circle, connecting two points on the circumference?

    <p>Diameter</p> Signup and view all the answers

    What is the name of the theorem that states that the angle at the center of a circle is twice the angle at the circumference?

    <p>Angle at the Center Theorem</p> Signup and view all the answers

    If a line is drawn from the center of a circle perpendicular to a chord, what does it do to the chord?

    <p>It bisects the chord</p> Signup and view all the answers

    What is the term for a straight line that touches the circle at only one point on the circumference?

    <p>Tangent</p> Signup and view all the answers

    What can be said about the opposite angles of a cyclic quadrilateral?

    <p>They are supplementary</p> Signup and view all the answers

    What is the relationship between the radius and the tangent at the point of contact?

    <p>The radius is perpendicular to the tangent</p> Signup and view all the answers

    What is the name of the theorem that states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?

    <p>Theorem of Pythagoras</p> Signup and view all the answers

    What is the angle between a tangent to a circle and a chord drawn from the point of contact equal to?

    <p>The angle subtended by the chord in the alternate segment</p> Signup and view all the answers

    If two chords are equal, what can be said about the angles subtended by them at the center of the circle?

    <p>They are equal</p> Signup and view all the answers

    What is the characteristic of a line segment from the center of a circle that bisects a chord?

    <p>It is perpendicular to the chord</p> Signup and view all the answers

    What is the relationship between the angles subtended by two arcs on the same side of the circle?

    <p>They are equal</p> Signup and view all the answers

    What can be said about the opposite angles of a cyclic quadrilateral?

    <p>They are supplementary</p> Signup and view all the answers

    What is the term for the part of the circle that is cut off by a chord?

    <p>Segment</p> Signup and view all the answers

    What can be said about the length of two tangents drawn from the same point outside a circle?

    <p>They are equal</p> Signup and view all the answers

    What is the special chord that passes through the center of the circle, connecting two points on the circumference?

    <p>Diameter</p> Signup and view all the answers

    What is the definition of a circumference?

    <p>The perimeter or boundary line of a circle</p> Signup and view all the answers

    What is the condition for a quadrilateral to be cyclic?

    <p>All its vertices lie on the circumference of a circle</p> Signup and view all the answers

    What can be said about the angle subtended by a chord at the center of a circle?

    <p>It is twice the angle subtended by the chord at the circumference</p> Signup and view all the answers

    What is the characteristic of a chord that passes through the center of a circle?

    <p>It is a diameter of the circle</p> Signup and view all the answers

    What is the relationship between the exterior angle of a cyclic quadrilateral and the interior opposite angle?

    <p>They are supplementary</p> Signup and view all the answers

    What is the definition of a segment of a circle?

    <p>A part of the circle that is cut off by a chord</p> Signup and view all the answers

    What is the condition for a line to be a tangent to a circle?

    <p>It touches the circle at one point</p> Signup and view all the answers

    What is the relationship between the angles subtended by a chord on the same side of the chord?

    <p>They are equal</p> Signup and view all the answers

    What is the angle formed by a tangent to a circle and the radius drawn to the point of contact?

    <p>90°</p> Signup and view all the answers

    What is the relationship between the lengths of two chords subtending equal angles at the center of a circle?

    <p>They are equal</p> Signup and view all the answers

    What is the sum of the interior opposite angles of a cyclic quadrilateral?

    <p>180°</p> Signup and view all the answers

    What is the relationship between the radius and a chord that passes through its midpoint?

    <p>The radius is perpendicular to the chord</p> Signup and view all the answers

    What is the ratio of the angle at the center of a circle to the angle at the circumference subtended by the same arc?

    <p>2:1</p> Signup and view all the answers

    What is the characteristic of the perpendicular bisector of a chord?

    <p>It passes through the center of the circle</p> Signup and view all the answers

    What is the relationship between the exterior angle of a cyclic quadrilateral and the interior angle adjacent to it?

    <p>They are supplementary</p> Signup and view all the answers

    What is the condition for a quadrilateral to be inscribed in a circle?

    <p>All vertices lie on the circumference of a circle</p> Signup and view all the answers

    What is the angle subtended by a chord at the center of a circle, if the angle subtended by the chord in the alternate segment is 30°?

    <p>60°</p> Signup and view all the answers

    What is the relationship between the length of two chords subtending equal angles at the center of a circle?

    <p>They are equal</p> Signup and view all the answers

    What is the characteristic of a line segment that joins the center of a circle and the midpoint of a chord?

    <p>It is perpendicular to the chord</p> Signup and view all the answers

    What is the condition for two points to be cyclic?

    <p>The angle subtended by them at the circumference is equal</p> Signup and view all the answers

    What is the relationship between the angles subtended by two arcs on the same side of the circle?

    <p>They are equal</p> Signup and view all the answers

    What is the characteristic of a line segment from the center of a circle that bisects a chord?

    <p>It is perpendicular to the chord</p> Signup and view all the answers

    What is the relationship between the length of two tangents drawn from the same point outside a circle?

    <p>They are equal</p> Signup and view all the answers

    What is the characteristic of the angle subtended by a diameter at the center of a circle?

    <p>It is right</p> Signup and view all the answers

    If two arcs of the same circle subtend equal angles at the center, what can be said about the chords that correspond to these arcs?

    <p>The chords are equal in length.</p> Signup and view all the answers

    What is the maximum number of tangent lines that can be drawn to a circle from a point outside the circle?

    <p>Two</p> Signup and view all the answers

    If a chord is drawn in a circle and the angle subtended by the chord at the center is 60°, what is the measure of the angle subtended by the chord in the alternate segment?

    <p>30°</p> Signup and view all the answers

    What is the relationship between the angles subtended by two arcs on the same side of a circle?

    <p>They are equal.</p> Signup and view all the answers

    If a line segment is drawn from the center of a circle to a point on the circumference, what is the relationship between this line segment and the tangent drawn to the circle at that point?

    <p>The line segment is perpendicular to the tangent.</p> Signup and view all the answers

    What is the condition for a quadrilateral to be inscribed in a circle?

    <p>The opposite angles are supplementary.</p> Signup and view all the answers

    If two chords of a circle are equal in length, what can be said about the angles subtended by these chords at the center of the circle?

    <p>The angles are equal.</p> Signup and view all the answers

    What is the relationship between the radius of a circle and the tangent drawn to the circle at a point on the circumference?

    <p>The radius is perpendicular to the tangent.</p> Signup and view all the answers

    If two chords intersect inside a circle, what is the relationship between the angles they subtend at the center of the circle?

    <p>The angles are equal</p> Signup and view all the answers

    If a line segment from the center of a circle bisects a chord, what can be said about the angle it forms with the chord?

    <p>The angle is a right angle</p> Signup and view all the answers

    If two chords are equal, what can be said about the angles they subtend at points on the circle?

    <p>The angles are equal</p> Signup and view all the answers

    If a line segment joins the center of a circle and the midpoint of a chord, what can be said about the angle it forms with the chord?

    <p>The angle is a right angle</p> Signup and view all the answers

    If two tangents are drawn from the same point outside a circle, what can be said about the angles they form with the radius drawn to the point of contact?

    <p>The angles are equal</p> Signup and view all the answers

    If a chord subtends an angle of 60° at the center of a circle, what can be said about the angle it subtends in the alternate segment?

    <p>The angle is 30°</p> Signup and view all the answers

    If two chords subtend equal angles at the center of a circle, what can be said about the lengths of the chords?

    <p>The lengths are equal</p> Signup and view all the answers

    If a line segment is perpendicular to a chord, what can be said about the angle it forms with the tangent drawn to the point of contact?

    <p>The angle is a right angle</p> Signup and view all the answers

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