New
New
Year 10
Higher

The tangents from an external point are equal in length

I can derive and use the theorem: the tangents from an external point are equal in length.

New
New
Year 10
Higher

The tangents from an external point are equal in length

I can derive and use the theorem: the tangents from an external point are equal in length.

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Lesson details

Key learning points

  1. A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
  2. Theorems can be thought of as puzzles to solve, you are showing how to find a result
  3. In order to use this theorem, you may need to draw a diagram or add more information to an existing one

Keywords

  • Tangent - A tangent of a circle is a line that intersects the circle exactly once.

  • Chord - A chord is any line segment joining two points on the circumference of a circle.

  • Perpendicular - Two lines are perpendicular if they meet at right angles.

  • Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.

Common misconception

Pupils may think that all circle theorems are about angles.

Circle theorems can be about angles or lengths in diagrams containing a circle.

The lesson demonstrates how this circle theorem could be explored practically by using a circular geoboard and using dynamic geometry software. Pupils may wish to explore these further for themselves.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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6 Questions

Q1.
The size of the angle labelled $$a$$° is °.
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Correct Answer: 54, 54°, 54 degrees
Q2.
The size of the angle labelled $$b$$° is °.
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Correct Answer: 50, 50°, 50 degrees
Q3.
∠ATC = 51° ∠ABT is subtended by the chord AT. The size of the angle labelled $$e$$° is °.
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Correct Answer: 51, 51°, 51 degrees
Q4.
∠PEF is subtended by the chord PF. ∠PFE is subtended by the chord PE. Find ∠EPD (in degrees).
An image in a quiz
48°
62°
Correct answer: 70°
90°
Not enough information.
Q5.
The size of angle $$c$$° is °.
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Correct Answer: 72, 72°, 72 degrees
Q6.
Find the size of angle $$d$$° (in degrees).
An image in a quiz
Correct Answer: 144, 144°, 144 degrees

6 Questions

Q1.
A triangle is formed on the circle from a segment of a tangent, a radius and another line segment. The size of angle $$a$$° is °.
An image in a quiz
Correct Answer: 67, 67°, 67 degrees
Q2.
Points T and U are points where two separate tangents intersect the circle. Find the size of angle $$b$$° (in degrees).
An image in a quiz
Correct Answer: 74, 74°, 74 degrees
Q3.
Points G and H are points where two separate tangents intersect the circle. The size of angle $$c$$° is °.
An image in a quiz
Correct Answer: 55, 55°, 55 degrees
Q4.
Points Q and P are points where two separate tangents intersect the circle. The size of the angle labelled $$d$$° is °.
An image in a quiz
Correct Answer: 50.5, 50.5°, 50.5 degrees
Q5.
Points J and K are points where two separate tangents intersect the circle. The size of angle $$e$$° is °.
An image in a quiz
Correct Answer: 96, 96°, 96 degrees
Q6.
Points L and N are points where two separate tangents intersect the circle. ∠LMN = 118°. $$g$$° = °.
An image in a quiz
Correct Answer: 56, 56°, 56 degrees, 56degrees