Circle

Question 1

Tangents to circles

Answer 1

Form right angle with line from tangent point to centre, creating a right angle triangle

Question 2

If circle touches x axis

Answer 2

x axis is a tangent therefore the radius = k from (h, k)

Question 3

If circle touches y axis

Answer 3

y axis is a tangent therefore the radius = h from (h,k)

Question 4

Touching externally

Answer 4

|c1 c2| = r1 + r2

Question 5

Touching internally

Answer 5

|c1 c2| = r1 - r2

Question 6

How to find equation with point and the centre

Answer 6

radius = |centre to point| then fill in formula

Question 7

How to find eq of circle with
-tangent
-point on tangent and circle
-other point on circle

Answer 7

1. Perp eq of line to tangent on point
2. Find slope of chord between 2 points
3. Find middle point of 2 points
4. Use perp slope of chord and middle point to find another eq of line
5. Line from steps 1 and 4 intersect at centre