The chords AB and CD of a circle with centre O and radius 25 cm are equal, and each is 14 cm long…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The chords and of a circle with centre and radius are equal, and each is long. Show that the two chords are at the same distance from , and find that distance.
Need a reminder? The key ideaShow
The perpendicular from the centre to a chord bisects the chord, and Pythagoras gives . Equal chords are equally far from the centre, and chords equally far from the centre are equal. A nearer chord is longer.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The equal parts.
- and , because the perpendicular from the centre bisects a chord.
- , the radii.
- .
Step 2. The rule. by RHS. So by CPCT.
Step 3. The number. , so .
Answer: each chord is from the centre.
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