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Chapter 9: Tangents and Secants to a Circle

    Introduction

    Tangents of a Circle

    Number of Tangent to a Circle From Any Point

    Segment of a circle Formed by a Secant

    Summary

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 9: Tangents and Secants to a Circle > Segment of a circle Formed by a Secant

Segment of a circle Formed by a Secant

Segments

The last part of a circle that we can find the area of is called a segment, not to be confused with a line segment. A segment of a circle is the area of a circle that is bounded by a chord and the arc with the same endpoints as the chord.

Now let us take the case of the area of the segment APB of a circle with centre O and radius r.

We can see that :

Area of the segment APB = Area of the sector OAPB – Area of ∆ OAB

= θ360·π·r2- Area of ∆ OAB

We can also observe that :

Area of the major sector OAQB = πr2 – Area of the minor sector OAPB

Area of major segment AQB = πr2 – Area of the minor segment APB

2. Find the area of the segment AYB, if radius of the circle is 21 cm and ∠AOB= 120°.

Find the area of segment

  • Area of the segment AYB = Area of sector OAYB – Area of △OAB
  • Now, finding the area of the sector OAYB, we get:
  • Calculate the segment then we get the answer is equal to cm2
  • We have found the answer.