Circle Tactics What is to be learned Tactics

Circle Tactics

What is to be learned? • Tactics for tackling circle questions

Basic Tactics If given an equation find Centre Radius If finding equation need Centre Radius Draw diagrams Straight line stuff vital

Terminology Concentric circles? Same centre Congruent Same shape and size

Proving Circles Touch Externally Given equations Get centre and radius Distance between centres = sum of radii Distance formula

Proving Circles Touch Internally Given equations Get centre and radius Distance between centres = difference between radii Distance formula

Circle Tactics If given an equation find Centre using x 2 + y 2 + 2 gx + 2 fy + c = 0 Radius (unless equation given with brackets) If finding equation need Centre Radius using (x – a)2 + (y – b)2 = r 2 Draw diagrams Straight line stuff vital - especially distance formula

Concentric circles- Same Centre Congruent- Same size Proving circles touch at one point - Externally Dist between centres = Sum of Radii

Proving Circles Touch Internally Distance between centres = difference between radii

Reminder Perpendicular Bisector cut line in half at right angles x 1+x 2 y 1+y 2 2 2 m 1 m 2 = -1

Equation from 3 Points mid pt m 1 m 2 = -1 Perpendicular Bisectors Centre – Point of Intersection Radius Distance Formula

Using Common Sense! A(2 , 6) and B are diametrically opposite Centre is (5 , 13) B? B (8, 20) 7 (5, 13) 3 7 (2, 6) 3 use steps

Closest Distance Closest distance between 2 circles (given equations) ? Dist between centres – (sum of radii)