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How do you prove tangents to external points?

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How do you prove tangents to external points?

PT and QT are two tangents drawn from an external point T to the circle C(O,r).

  1. To Prove: PT=TQ.
  2. ∴∠OPT=∠OQT=90∘
  3. ∠OPT=∠OQT(90∘)
  4. OT=OT (common)
  5. OP=OQ (Radius of the circle)
  6. ∴△OPT≅△OQT (By RHS criterian)
  7. So, PT=QT (By CPCT)

How many tangents can be drawn to a circle from an external point?

two tangents
It may be noted that from a particular point outside a circle only two tangents can be drawn.

What are the properties of the tangents drawn to a circle from an external point?

1) The length of two of tangents drawn from an external point to a circle are equal. 2) The length of two of tangents drawn from an external point to a circle are equal. 3) The length of two of tangents drawn from an external point to a circle are equal. 5) Subtract AD on both sides.

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How many tangents can a circle have *?

infinite tangents
Circle is the locus of points equidistant from a given point, which is the centre of the circle. And, tangent is the line which intersects a circle at one point only. on these points which touches at only one point. Hence, a circle can have infinite tangents.

How do you prove two tangents are congruent?

A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency. The Two-Tangent Theorem states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.

How do you find tangent properties?

Properties of Tangents

  1. The tangent line never crosses the circle, it just touches the circle.
  2. At the point of tangency, it is perpendicular to the radius.
  3. A chord and tangent form an angle and this angle is same as that of tangent inscribed on the opposite side of the chord.
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How do you draw a tangent to a circle?

Point to Tangents on a Circle

  1. Draw a line connecting the point to the center of the circle.
  2. Construct the perpendicular bisector of that line.
  3. Place the compass on the midpoint, adjust its length to reach the end point, and draw an arc across the circle.
  4. Where the arc crosses the circle will be the tangent points.