Geometrical Reasoning
Key Stage: 4 ★★
A circle has its centre on the hypotenuse of a right angled triangle, and touches the other two sides. Can you relate its radius to the side lengths of the triangle?
This problem offers students a valuable context in which to visualise the effect of constraints . They can be encouraged to establish the relationships within the context (for example by utilising properties of similar triangles), and then find a way to use those to make a route to a solution, which might include working backwards as well as algebraic manipulation.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
Key Stage: 4 ★★
A circle has its centre on the hypotenuse of a right angled triangle, and touches the other two sides. Can you relate its radius to the side lengths of the triangle?
This problem offers students a valuable context in which to visualise the effect of constraints . They can be encouraged to establish the relationships within the context (for example by utilising properties of similar triangles), and then find a way to use those to make a route to a solution, which might include working backwards as well as algebraic manipulation.
This resource has comprehensive teachers' notes and resources, linked from the problem page. This includes possible approaches and key questions, as well as possible support and extensions.
The file attached is a HTML file, which, when opened, automatically redirects you to the problem on the NRICH website.
Something went wrong, please try again later.
Very challenging task for GCSE students, possibly useful for A level also - in particular, when covering coordinate geometry. The task involves proving a result based on the information given in the question.
Report this resourceto let us know if it violates our terms and conditions.
Our customer service team will review your report and will be in touch.
£0.00