Lines & portion associated to a Circle.
Let’s see the geometrical
lines & portions associated with the circle which helps to solve the
problems.
Tangent.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhx7iaQssf5lb9tVcRPSlH9glV5VlNGP1pXQzzXYWvRxWog76FJoj99wkhdQOZ1bIEgeLbiQsIBjVz96Otwcc9OqfMzRY6csrLnMZwiORekDpbUiv9iS4rwqrfFZ6r6cYh_tMwj8_nhpg4/s320/0001.jpg)
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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYPdGMdHoW_HMcfAq7qy96ZNg32PjmSRZIVObwtuCswcslo4F2zbkWkh3JOAA175I7y30uK2zwydMhhvctoUAPsdlbRNyisa1rccdsD7D6CQMTXWJrmMEZ2wNVRM-e2DHigJ2NCavRU5A/s320/2.jpg)
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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiY-0Om4HWR9OBs7ytGGj2mYJvp7eJAv8TQyw2wBUbOv0zwqfbIjvC3Ww1bFI4XpviL5X894Nt88wI-yE_TvLsucoPZsSrwCtzpekHjm0IwvYswZJ4R-IzK09L2fa7hzOr87Jk0jZ_lgrk/s320/4.jpg)
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.
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