Tangent, Secant, Chord, Arc, Sector & Segment of Circle.

Lines & portion associated to a Circle.

Let’s see the geometrical lines & portions associated with the circle which helps to solve the problems.

Tangent.

Tangents can be defined as a straight line that just touches the curve only at one point and this point of contact is known as point of tangency. The angle of intersection between the radius/diameter of the circle with tangent is 90 degree.

Tangent in daily life.

Imagine that you have a bicycle and you are riding it in a flat ground. On analyzing the situation, the wheel of the bicycle is in circular shape, the spoke which is supporting the wheel will be its radius, the flat ground where you are riding the bicycle become the tangent and the point of contact between the wheel and the flat ground become the point of tangency.

Always the point to be noted that the radius of the circle will be perpendicular to the tangent.

Secant, Chord and diameter

Secant can be defined as the line which intersect the circle at two different point. The chord is segment of a secant between the intersecting points of the circle or secant is the infinite line extension of chord. If the chord passes through the center of the circle then it became the diameter of the circle, which is the longest chord of the circle.

Intersecting Secants Theorem.

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

That is MN x MO = MP x MQ

Arc of a circle

We know that a circle is at 360 degree all the way around, if you divide the circle you will get a fraction of circumference of the circle with an inscribed angle ‘θ’ to the center which is known as Arc of a circle. The length of the Arc can be found from the following formula.

Arc length, AB = r x θ.     

         Where r = radius of the circle

      θ = Arc angle.

Circular Sector.

It can be defined as the portion of the circle formed by an arc and two radius having central angle. If the two radius equals the diameter and the central angle equals 180 degree then the sector is called as Semicircle. Area of a sector can be found by using the below formula,

Area of a sector, AOB = r² x θ/2

Segment of a circle.

It can be defined as the portion of circle circumscribed by chord and Arc or it can be defined as the portion of a sector from which the area of the triangle formed by the radii is removed.

Area of segment = Area of sector – Area of triangle.

Understanding the basics makes easier to do complex problems.

Thank you.