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You will need to know about similarity of triangles to solve this problem. Figure shows the position of a lizard L on the ceiling of a room. Determine the shortest possible distance AL such that the eye can see the lizard in the mirror. 
question image
Asked by officeofhng | 24 Aug, 2018, 05:47: PM
answered-by-expert Expert Answer
Figure shows the image of lizard seen by the eye when AL is shortest distance and
reflection is taking place at the top most point B of mirror.
 
begin mathsize 12px style angle L B C space equals space angle E B C space end style, because reflection is taking place at B and angle of incidence is equla to angle of reflection.
Since ΔLBC and ΔEBD are right angled triangle and due to the equalness of angles mentioned above,
ΔLBC begin mathsize 12px style approximately equal to end style ΔEBD
begin mathsize 12px style fraction numerator E D over denominator L C end fraction equals fraction numerator B D over denominator B C end fraction equals 5 over 7 end style..............(1)
Hence from (1), we get BC = 100 cm,  or BC=AL=100 cm
Answered by Thiyagarajan K | 25 Aug, 2018, 11:33: AM

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