In the given, figure, CD and AB are diameters of circle and AB and CD are perpendicular to each other, LQ and SR are perpendiculars to AB and CD respectively. Radius of circle is 5 cm, PB : PA = 2 : 3. What is the length (in cm) of SM?
A. $$\left[ {\left( {5\sqrt 3 } \right) - 3} \right]$$
B. $$\left[ {\left( {4\sqrt 3 } \right) - 2} \right]$$
C. $$\left[ {\left( {2\sqrt 5 } \right) - 1} \right]$$
D. $$\left[ {\left( {2\sqrt 6 } \right) - 1} \right]$$
Answer: Option D
Solution (By Examveda Team)
O is the center of circle and radius is 5 cm.
PB : PA = 2 : 3 (Given)
PB + PA = 10 cm (Diameter)
∴ 2 + 3 = 5 units → 10 cm
1 unit → 2 cm
∴ PB = 4 cm
PA = 6 cm
OP = AP - OA
AP = 6 cm, OA = 5 cm (Radius)
∴ OP = 6 - 5 = 1 cm
Similarly ON = 1 cm
In ΔONS
Use pythagoras theorem
SO2 = NO2 + NS2
25 = 1 + NS2
NS2 = 24
NS = $$\sqrt {24} $$
∴ SM = NS - MN
∴ MN = OP = 1 cm
SM = $$\sqrt {24} - 1$$
SM = $$\left[ {\left( {2\sqrt 6 } \right) - 1} \right]$$ cm
This Question Belongs to Arithmetic Ability >> Geometry
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