Flash Cards: Circles
Circles - Flash Cards
1/19
What is a circle?
1/19
A circle is a collection of all points in a plane which are at a constant distance (radius) from a fixed point (centre).
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2/19
What is a chord in a circle?
2/19
A chord is a straight line segment whose endpoints lie on the circle.
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3/19
What is a secant?
3/19
A secant is a line that intersects the circle at two points.
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4/19
What is a tangent?
4/19
A tangent is a line that intersects the circle at exactly one point.
5/19
What are the types of positions a line can have with respect to a circle?
5/19
A line can be a secant, a tangent, or a non-intersecting line.
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What is the point of contact?
6/19
The point of contact is the point where a tangent touches the circle.
7/19
State Theorem 10.1.
7/19
The tangent at any point of a circle is perpendicular to the radius through the point of contact.
8/19
How many tangents can be drawn from a point outside a circle?
8/19
Exactly two tangents can be drawn from a point outside a circle.
9/19
Can a tangent be drawn from a point inside the circle?
9/19
No, a tangent cannot be drawn from a point inside the circle.
10/19
What is the relationship between chords and tangents?
10/19
A tangent to a circle is a secant when both end points of its corresponding chord coincide.
11/19
What is the maximum number of parallel tangents to a circle?
11/19
A circle can have a maximum of two parallel tangents.
12/19
What is the length of the tangent from a point to a circle?
12/19
The length of the tangent from an external point to the circle can be determined using the formula: √(d² - r²), where d is the distance from the point to the center and r is the radius.
13/19
What happens to the lengths of tangents drawn from an external point to a circle?
13/19
The lengths of the two tangents drawn from an external point to a circle are equal.
14/19
How is a tangent related to the radius at the point of contact?
14/19
The radius drawn to the point of contact is perpendicular to the tangent.
15/19
What can be said about two tangents drawn from an external point?
15/19
The angle between the two tangents is supplementary to the angle subtended by the line segment joining the points of contact at the center.
16/19
What is the property of a chord that touches another concentric circle?
16/19
The chord of a larger circle, which touches a smaller concentric circle, is bisected at the point of contact.
17/19
Write down the equation of a circle with centre (0, 0) and radius r.
17/19
The equation of a circle is x² + y² = r².
18/19
Is a tangent unique at a point on the circle?
18/19
Yes, there is only one tangent at any given point on the circle.
19/19
What does it mean if a line is non-intersecting with a circle?
19/19
A non-intersecting line does not touch or cross the circle at any point.
