A bike-share dock has a circular base of centre \(O\) and radius \(4\) metres. From a parking point \(P\), two straight guide rails run out to touch the doc...
Question 1 Report
A bike-share dock has a circular base of centre \(O\) and radius \(4\) metres. From a parking point \(P\), two straight guide rails run out to touch the dock's rim, one at \(T\) and the other at \(S\); each rail is \(9\) metres long.
Work out the total length of wire needed to fence the outline \(O\) to \(T\) to \(P\) to \(S\) to \(O\). (3)
Answer Details
The two tangent segments from a single external point to the same circle are always equal in length, so both guide rails here must be the same length as each other.
\(OT\) and \(OS\) are both radii, so \(OT = OS = 4\) metres; \(PT\) and \(PS\) are both tangents from the same external point \(P\), so \(PT = PS = 9\) metres. [1 mark]
The outline \(O\) to \(T\) to \(P\) to \(S\) to \(O\) is made up of these four segments in turn: \(OT + TP + PS + SO\). [1 mark] Adding them, the total length is \(4 + 9 + 9 + 4 = 26\) metres. [1 mark]
Exam tip: for a perimeter built from radii and tangents, identify which segments are radii (always equal to each other) and which are tangents from the same point (also always equal to each other) before adding; it avoids having to measure or recompute each one separately.
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