How many common points do a circle and a straight line have if the radius of the circle is 5√12 cm, and the distance

| December 25, 2020 | education

How many common points do a circle and a straight line have if the radius of the circle is 5√12 cm, and the distance from the center of the circle to the straight line is: a) 6√8 cm; b) 10√3 cm; c) 12√5 cm; d) 15√2 cm?

Rules: If the distance from the center of the circle to the straight line is less than the radius of this circle, then the straight line and the circle intersect at two points. If the distance from the center of the circle to the straight line is greater than the radius of this circle, then the straight line and the circle do not intersect. If the distance from the center of the circle to the straight line is equal to the radius of this circle, then the straight line and the circle touch at 1 point. a) d = 6√8 = 12√2 cm; r = 5√12 = 10√3 cm 12√2 cm <10√3 cm (√288 <√300) -> d <r. This means that the line and the circle intersect at two points. b) d = 10√3 cm, r = 10√3 cm, d = r -> a straight line and a circle touch at 1 point. c) d = 12√5 cm, r = 10√3 cm, d> r -> line and circle do not intersect; d) d = 15√2 cm, r = 10√3 cm, d> r -> line and circle do not intersect.
Answer: a) 2 points b) 1 point c) no intersection points d) no intersection points



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