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10th Class Chapter No 17 - Circle : Tangents and Intersecting Chords in Maths for ICSE

Tangent to a circle

  • A tangent line to a circle is a line that touches the circle at exactly one point. 
  • A tangent to a circle is perpendicular to the radius at the point of tangency.

Theorem 1 : The tangent of a circle is perpendicular

If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.

Theorem 2: Two tangents Theorem

If two tangents are drawn to a circle from an exterior point (the points which lies outside the circle):

  1. The tangents are equal in length
  2. The tangent subtend equal angles at the center  of the circle and
  3. The tangents are equally inclined to the line joining the point and the center of the circle.

Theorem : 3

If two circles touch each other, the point of contact lies on the straight line through the centres.
 

Intersecting Chords Theorem 1

If two chords of a circle intersect internally or externally, then the product of the lengths of their segments is equal.

  • For the chords intersecting internally, EA ×× EB = EC ×× ED
  • For the chords intersecting externally, EA ×× EB = EC ×× ED

Theorem 2(Alternate segment theorem)

The angle between a tangent and a chord through the point of contact is equal to an angle in the alternate segment.

  • PTS = SRT
  • PTU = UST

Theorem 3

If a chord and a tangent intersect externally, then the product of the lengths of the segment of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.


 

Posted in 10th on July 11 2020 at 07:11 AM

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