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Math(F4) Circle Iii 8.1

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A tangent to a circle is perpendicular to the radius drawn through the contact point. A tangent to a circle is a straight line which touches the circle at only one point. The lengths of the tangents drawn from a point outside the circle to the contact points are equal, and the angles formed between the tangents and radii are congruent.

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8 Chapter CIRCLE III
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8.1 (a) Identify Tangents
P A Q Circle Straight Line Intersection at point A What is tangent ?
When a circle and a straight line intersect at 1 point, we called that line as a tangent .
P A Q Tangent to a circle
Is this a tangent ? Tangent to a circle A B C
Is this a tangent ? Tangent to a circle X Y Z
Which are tangents to a circle ? A C D F E O H B G Answer : Tangent CD at point A Tangent GH at point B
Which are tangents to a circle ? Answer : Tangent AB at point H Tangent AC at point E A E D C B H F G Tangent BD at point G
Hiii… Everyone, are you ready to learn the next lesson.. ?
Next concept
Tangent to a circle is perpendicular to the radius of the circle that passes through the contact point .
P Q Tangent to a circle Radius 90 0 = perpendicular
P O R Q Tangent PQ perpendicular with radius OP. Tangent RQ perpendicular with radius OR.
8.1 (b) Construct the tangent to a circle passing through a point : a) on the circumference of the circle b) outside the circle
Activity 1 ( Construct the tangent to a circle passing through a point on the circumference of the circle ) Form a group of 5 students. Complete activity 1 by using roundtable method. Time given is 5 minutes. Then, a student will be chosen to present the work in front.
Activity 2 ( Construct the tangent to a circle passing through a point outside the circle ) Form a group of 5 students. Complete activity 2 by using roundtable method. Time given is 3 minutes. Then, a student will be chosen to present the work in front.
The Properties Related To Two Tangents From A Given Point Outside The Circle 8.1c
What is The Properties Related To Two Tangents From A Given Point Outside The Circle? Let’s do this activity together
1. Use the previous figure and construct segment from centre to the contact point on the circumference of the circle.
2. Using a ruler and a protractor, measure and record the lengths and angles in table. Value Angle Length
What do you get from this activity? 1. The lengths of the tangent from a given point A to each contact point are equal, PA = QA 2. The line that joins the given point outside the circle, point A , to the centre of the circle bisects. a) the angle between the two tangents, that is, b) the angle between the two radii that passes through the contact points, that is,
3. are congruent.
SUMMARY A tangent to a circle is ____________ to the radius drawn through the _________ A tangent to a circle is a __________ ____________________________ O A c O B C AB and AC are _______ to the ________ AC BC OBC and OAC are ___________
SUMMARY A tangent to a circle is perpendicular to the radius drawn through the contact point . A tangent to a circle is a straight line which touches the circle at a point. A c O B C AB and AC are tangents to the circle . AC = BC OBC and OAC are congruent . O

More Related Content

Math(F4) Circle Iii 8.1

  • 8. 8.1 (a) Identify Tangents
  • 9. P A Q Circle Straight Line Intersection at point A What is tangent ?
  • 10. When a circle and a straight line intersect at 1 point, we called that line as a tangent .
  • 11. P A Q Tangent to a circle
  • 12. Is this a tangent ? Tangent to a circle A B C
  • 13. Is this a tangent ? Tangent to a circle X Y Z
  • 14. Which are tangents to a circle ? A C D F E O H B G Answer : Tangent CD at point A Tangent GH at point B
  • 15. Which are tangents to a circle ? Answer : Tangent AB at point H Tangent AC at point E A E D C B H F G Tangent BD at point G
  • 16. Hiii… Everyone, are you ready to learn the next lesson.. ?
  • 18. Tangent to a circle is perpendicular to the radius of the circle that passes through the contact point .
  • 19. P Q Tangent to a circle Radius 90 0 = perpendicular
  • 20. P O R Q Tangent PQ perpendicular with radius OP. Tangent RQ perpendicular with radius OR.
  • 21. 8.1 (b) Construct the tangent to a circle passing through a point : a) on the circumference of the circle b) outside the circle
  • 22. Activity 1 ( Construct the tangent to a circle passing through a point on the circumference of the circle ) Form a group of 5 students. Complete activity 1 by using roundtable method. Time given is 5 minutes. Then, a student will be chosen to present the work in front.
  • 23. Activity 2 ( Construct the tangent to a circle passing through a point outside the circle ) Form a group of 5 students. Complete activity 2 by using roundtable method. Time given is 3 minutes. Then, a student will be chosen to present the work in front.
  • 24. The Properties Related To Two Tangents From A Given Point Outside The Circle 8.1c
  • 25. What is The Properties Related To Two Tangents From A Given Point Outside The Circle? Let’s do this activity together
  • 26. 1. Use the previous figure and construct segment from centre to the contact point on the circumference of the circle.
  • 27. 2. Using a ruler and a protractor, measure and record the lengths and angles in table. Value Angle Length
  • 28. What do you get from this activity? 1. The lengths of the tangent from a given point A to each contact point are equal, PA = QA 2. The line that joins the given point outside the circle, point A , to the centre of the circle bisects. a) the angle between the two tangents, that is, b) the angle between the two radii that passes through the contact points, that is,
  • 29. 3. are congruent.
  • 30. SUMMARY A tangent to a circle is ____________ to the radius drawn through the _________ A tangent to a circle is a __________ ____________________________ O A c O B C AB and AC are _______ to the ________ AC BC OBC and OAC are ___________
  • 31. SUMMARY A tangent to a circle is perpendicular to the radius drawn through the contact point . A tangent to a circle is a straight line which touches the circle at a point. A c O B C AB and AC are tangents to the circle . AC = BC OBC and OAC are congruent . O