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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.

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Tangents to a Circle

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  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

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