Tangents and Chords

Tangents and Chords

Tangents

In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle’s interior.

A line which touches a circle or ellipse at just one point. Below, the line L is a tangent to the circle c. Note the radius to the point of tangency is always perpendicular to the tangent line. The method for finding the gradient uses the fact that the tangent is perpendicular to the radius from the point it meets the circle. Work out the gradient of the radius at the point the tangent meets the circle, and you can use the equation mCP x mtgt = -1 to find the gradient of the tangent.

Exactly 0 tangents can be drawn through a circle. A tangent intersects a circle in only one point so it does not actually enter the area of the circle. An infinite number of tangents to a given circle can be drawn since their is no limit to the points a tangent could intersect.

Chords

A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite line extension of a chord. More generally, a chord is a line segment joining two points on any curve, for instance an ellipse.

A line segment connecting two points on a curve. Example: the line segment connecting two points on a circle’s circumference is a chord. When the chord passes through the center of a circle it is called the diameter. See: Diameter. Circle.

If you know the radius and the perpendicular distance from the center of the circle to the chord, the formula would be: This formula is essentially a variation of the Pythagorean theorem (a squared + b squared = c squared), with a and b being the sides of a right triangle and c being the hypotenuse.

Question 1: The line segment between the centre and a point on the circle

A) Radius

B) Diameter

C) Chord

D) Tangent

E) None of these

Answer : Radius

Question 2: Circles with exactly the same radius measures

A) Similar Circles

B) Concentric Circles

C) Congruent Circles

D) Semicircle

E) None of these

Answer : Congruent Circle

Question 3: Half of a circle or an arc that is 180 degrees

A) Major Arc

B) Minor Arc

C) Circle

D) Semicircle

E) None of these

Answer : Semicircle

Question 4: A line segment on interior of circle with end points on the circle

A) Radius

B) Diameter

C) Chord

D) Secant

E) None of these

Answer : Chord

Question 5: The distance around a circle

A) Diameter

B) Radius

C) Circumference

D) Area

E) None of these

Answer : Circumference