AS Pure Chapter 6: Circles

11 flashcards · Mathematics · by TheoTyson

1. What is the midpoint of a line segment with endpoints (x1,y1)(x_1, y_1)(x1​,y1​) and (x2,y2)(x_2, y_2)(x2​,y2​) ?

   (x1+x22,y1+y22)(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})(2x1​+x2​​,2y1​+y2​​)

2. What is the perpendicular bisector of line segment ABABAB ?

   Straight line that is perpendicular to ABABAB and passes through the midpoint of ABABAB .

3. What is the equation of a circle with centre (0,0)(0, 0)(0,0) and radius rrr ?

   x2+y2=r2x^2 + y^2 = r^2x2+y2=r2

4. What is the equation of a circle with centre (a,b)(a, b)(a,b) and radius rrr ?

   (x−a)2+(y−b)2=r2{(x-a)}^2 + {(y-b)}^2 = r^2(x−a)2+(y−b)2=r2

5. How many times can a straight line intersect a circle?

   Twice and pass through the circle, once and just touch the circle, or zero times.

6. What is a tangent?

   A straight line that intersects a curve at only one point.

7. What is a tangent to a circle?

   A tangent to a circle is perpendicular to the radius of the circle at the point of intersection.

8. What is a chord?

   A line segment that joins two points on the circumference of the circle.

9. What does a perpendicular bisector of a chord do?

   The perpendicular bisector of a chord will go through the centre of the circle.

10. What is special about a triangle subtended in a circle where one side is the diameter?

    The angle in the semicircle is 90°.

11. How do you find the centre of the circle from three points on the circumference?

    Find the point of intersection between the two perpendicular bisectors that can be formed from the line segments connecting the points.