Question 24
In the diagram, $r$ is the radius of the small circle with center $A$. $ABCD$ is a rectangle with $AB=5$ cm and $BC=12$ cm. Find the range of values of $r$.
Source limitation: the prose does not explicitly state the larger circle’s center, tangency or exact inside/outside conditions. The printed solution uses extra geometric assumptions and contains an inconsistent inequality step. Give a reasoned assessment of whether a unique range follows; identify any assumptions used for a conditional range. This response is assessed manually.
Original source figure, preserving its mathematical labels and arrangement.
Source limitation: the prose does not explicitly state the larger circle’s center, tangency or exact inside/outside conditions. The printed solution uses extra geometric assumptions and contains an inconsistent inequality step. Give a reasoned assessment of whether a unique range follows; identify any assumptions used for a conditional range. This response is assessed manually.
Original source figure, preserving its mathematical labels and arrangement.