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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Circle

Olympiad workbook · IOQM · Circle

Given a pair of concentric circles, chords A B, B C , C D, of the...

Given a pair of concentric circles, chords AB,BCA B, B C, CD,…C D, \ldots of the outer circle are drawn such that they all touch the inner circle. If ∠ABC=75∘\angle A B C=75^{\circ}, how many chords can be drawn before returning to the starting point? Given a pair of concentric circles, chords A B, B C , C D, of the outer circle are drawn such that they all touch the

Correct answer

24

Step-by-step solution

To reach same point, rotation shall be multiple of 360∘360^{\circ} and also angle formed at B,C,…B, C, \ldots. will be 75∘75^{\circ}. For reaching point AA say in nn points like as A,B,CA, B, C required n=LCM⁡(105∘,360∘)105∘=105×24105=24\begin{aligned} n & =\frac{\operatorname{LCM}\left(105^{\circ}, 360^{\circ}\right)}{105^{\circ}} \\ & =\frac{105 \times 24}{105}=24 \end{aligned}
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