Circle properties Quiz

1. $A=(0,0)$ and $B=(6,0)$ are the ends of a diameter. Which point is on the circle?

• A. $(3,3)$
• B. $(3,4)$
• C. $(6,3)$
• D. $(0,3)$

2. A chord has gradient $2$. What is the gradient of the line from the centre to its midpoint?

• A. $2$
• B. $-2$
• C. $\frac12$
• D. $-\frac12$

3. A circle has centre $(0,0)$. The gradient of the tangent at $(3,4)$ is

• A. $\frac43$
• B. $\frac34$
• C. $-\frac34$
• D. $-\frac43$

4. A chord of length $8$ lies in a circle of radius $5$. The distance from the centre to the chord is

• A. $1$
• B. $3$
• C. $4$
• D. $\sqrt{41}$

5. The circle $x^2+y^2=25$ has a tangent at $(5,0)$. Its equation is

• A. $y=5$
• B. $y=0$
• C. $x=0$
• D. $x=5$