1 / 19

Tangents to a Circle

Tangents to a Circle. A tangent to a circle. A. B. Tangents to A Circle. - a straight line which touches the circle at only one point. - perpendicular to the radius at the point of contact. AB = tangent to the circle. Constructing tangents to a circle.

trapper
Download Presentation

Tangents to a Circle

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Tangents to a Circle

  2. A tangent to a circle A B Tangents to A Circle - a straight line which touches the circle at only one point - perpendicular to the radius at the point of contact AB = tangent to the circle

  3. Constructing tangents to a circle The diagram below shows a circle with centre O. Construct the tangent to the circle at the point P. P O Tangents to A Circle

  4. Constructing tangents to a circle P O Tangents to A Circle Solution: Step 1: Draw a straight line joining point P and centre O.

  5. Constructing tangents to a circle P O Tangents to A Circle Solution: Step 2: Adjust your compasses so that its radius is slightly more than half of the length of OP.

  6. Constructing tangents to a circle P O Tangents to A Circle Solution: Step 3: Place your compasses at P. On the line OP, draw one point on both sides of P.

  7. Constructing tangents to a circle P O Tangents to A Circle Solution: Step 4: Place your compasses at one of the point on the line OP, draw an arc above and below the line OP.

  8. Constructing tangents to a circle P O Tangents to A Circle Solution: Step 5: With the same radius and another point on line OP as centre, draw another two arcs to intersect the ones drawn in step 4.

  9. Constructing tangents to a circle Tangent at P P O Tangents to A Circle Solution: Step 6: Join the two intersections with a straight line.

  10. Constructing tangents to a circle The diagram below shows a circle with centre O. Construct two tangents to the circle that pass through the point T. T O Tangents to A Circle

  11. Constructing tangents to a circle O Tangents to A Circle Solution: Step 1: Draw a straight line joining point T and centre O. T O

  12. Constructing tangents to a circle Tangents to A Circle Solution: Step 2: Adjust your compasses so that its radius is slightly more than half of the length of OT. T O

  13. Constructing tangents to a circle Tangents to A Circle Solution: Step 3: Place your compasses at T. Draw a short arc above and below the line OT. T O

  14. Constructing tangents to a circle Tangents to A Circle Solution: Step 4: With the same radius and your compasses placed at O, draw arcs to intersect the ones drawn in Step 3. T O

  15. Constructing tangents to a circle Tangents to A Circle Solution: Step 5: Join the two intersections with a straight line. T O

  16. Constructing tangents to a circle M Tangents to A Circle Solution: Step 6: Label the midpoint as M. Using M as the centre and OM as the radius, draw two arcs that cut the circle at P and Q. P T O Q

  17. Constructing tangents to a circle Lines PT and QT are tangents to the circle that pass through point T Tangents to A Circle Solution: Step 7: Join points P and Qto point T. P T M O Q

  18. Properties related to two tangents to a circle P y° x° T x° O y° Q Tangents to A Circle • PT = QT • PTO = OTQ • POT = QOT • ∆POT and ∆QOT are congruent.

  19. The End

More Related