Tangents to a Circle

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

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

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

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

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

Constructing 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. P O

Constructing 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. P O

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

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

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

Constructing 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

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

Constructing 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

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

Constructing 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 M Q

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

Properties related to two tangents to a circle Q y° x° PT = QT  PTO =  OTQ  POT =  QOT ∆POT and ∆QOT are congruent.

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