1. In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE:EB = 1:2, and DF is perpendicular to MN such that NL:LM = 1:2. The length of DH in cm is
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By: anil on 05 May 2019 02.29 am
Let EO = x, So, AE = 3/2 - x
AE : EB = 1:2 => x = 1/2
So, EO = 1/2
Similarly, OL = 1/2
Now, EOLH is a parallelogram and EO = OL = 1/2.
So, OL = 1/2
In triangle DOL, DO = radius = 3/2 and OL = 1/2
So, DL = $$sqrt2$$
=> DH = $$(2sqrt2 - 1)/2$$
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AE : EB = 1:2 => x = 1/2
So, EO = 1/2
Similarly, OL = 1/2
Now, EOLH is a parallelogram and EO = OL = 1/2.
So, OL = 1/2
In triangle DOL, DO = radius = 3/2 and OL = 1/2
So, DL = $$sqrt2$$
=> DH = $$(2sqrt2 - 1)/2$$