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How do you prove that the perpendicular at point of contact to tangent of circle passes through the center?

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How do you prove that the perpendicular at point of contact to tangent of circle passes through the center?

A tangent PR has been drawn touching the circle at point P. Draw QP ⊥ RP at point P, such that point Q lies on the circle. Now, the above case is possible only when centre O lies on the line QP. Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

What is point of contact Class 10?

CBSE NCERT Notes Class 10 Maths Circles. A tangent to a circle is a line that intersects the circle at only one point. The common point G of the tangent and the circle is called the point of contact and the tangent is said to touch the circle at the common point.

At which point a tangent is perpendicular to the circle?

Theorem – The tangent at any point of a circle is perpendicular to the radius through the point of contact – Circles | Class 10 Maths. Tangent is a straight line drawn from an external point that touches a circle at exactly one point on the circumference of the circle.

How do you prove tangents are perpendicular to Radius?

Tangent – Perpendicular to Radius

  1. Given:
  2. To prove: OP ⊥ XY.
  3. Construction: On XY take any point Q, other than P.
  4. Proof:
  5. One and only one tangent can be drawn to a circle at a given point on the circumference because only one perpendicular can be drawn to Op through the point P.

What is always perpendicular to the point of contact of a tangent?

As we know that, a tangent at any point of a circle is perpendicular to the radius through the point of contact. At the point of contact P, RP is perpendicular to the tangent PQ. We also know that the radius or diameter will always pass through the centre of the circle. Therefore, PR passes through the centre O.

Is a point at a distance 13 cm from the Centre of a circle of radius 5cm?

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C ,find the perimeter of the ΔABC.

How do you prove tangent theorem?

Theorem 1

  1. Construction: Draw a circle with centre O. Draw a tangent XY which touches point P at the circle.
  2. To Prove: OP is perpendicular to XY.
  3. Construction: Draw a circle with centre O. From a point P outside the circle, draw two tangents P and R.
  4. To Prove: PQ = PR.
  5. Proof: In Δ POQ and Δ POR.

What is tangent of a circle class 10?

Tangent to a Circle is a straight line that touches the circle at any one point or only one point to the circle, that point is called tangency. At the tangency point, the tangent of the circle will be perpendicular to the radius of the circle.

How do you prove tangents?

You will prove that if a tangent line intersects a circle at point \begin{align*}P\end{align*}, then the tangent line is perpendicular to the radius drawn to point \begin{align*}P\end{align*}. From any point outside a circle, you can drawn two lines tangent to the circle.

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

two tangents
Theorem: Exactly two tangents can be drawn from an exterior point to a given circle.

Is the perpendicular at the point of contact to the tangent to?

A tangent PR has been drawn touching the circle at point P. Draw QP ⊥ RP at point P, such that point Q lies on the circle. Now, above case is possible only when centre O lies on the line QP. Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Can a tangent pass through the centre of a circle?

A tangent PR has been drawn touching the circle at point P. Draw QP ⊥ RP at point P, such that point Q lies on the circle. Now, the above case is possible only when centre O lies on the line QP. Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Where does the perpendicular pass through a circle?

Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle. Was this answer helpful? Thank you. Your Feedback will Help us Serve you better.

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