Applications of Circles
Interactive practice questions
The radio tower on a navy vessel continuously sends out signals in every direction to pick up any other vessels within a $11$11 km radius.
Let the tower be positioned at $\left(0,0\right)$(0,0) on the plane.
A submarine is $9.1$9.1 km East and $7.1$7.1 km North of the tower. What is its direct distance from the tower?
Give your answer to one decimal place.
Will the radio tower's signals pick up the submarine?
No
Yes
Consider a circle with centre $O$O at $\left(0,0\right)$(0,0) that passes through the point $A\left(-7,6\right)$A(−7,6). A diameter is drawn from point $A$A to point $B$B on the circle.
State the coordinates of point $B$B.
Consider the diagram of the circle with centre $B$B and point $A$A$\left(3,3\right)$(3,3) on the circumference. $\triangle PAB$△PAB is such that $PA$PA is a horizontal interval with $PA=4$PA=4 and $PB=5$PB=5.
A point $P$P$\left(x,y\right)$(x,y) moves so that it is always $7$7 units from the point $\left(0,0\right)$(0,0).