Length of a line segment

Geometry Level 2

Find the length of the line segment CS in meter.


The answer is 8.

Jobayer Mahmud by Jobayer Mahmud , 29, Bangladesh

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2 solutions

Arun Ar
Jul 14, 2014

AD and ST are the diameters of the circle with center O. AB is chord of the circle. OC perpendicular to AB means it bisects AB. therefore, AB= BC= 4m

OC parallel BD and OC perpendicular to AB means triangle CBD is a right angled triangle right angled at B, area of triangle CBD is given and we get BD= 6m.

ABD is a right angled triangle right angled at B, we get AD=10m

using Pythagoras theorem AD = ST = 10m OS =OT = OA = OD =5m

triangle ACO is a right angled triangle right angled at C, using Pythagoras theorem OC= 3m

CS= OS + OC = 5 + 3 = 8m

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Arun, please edit on the second line of your solution. Its AC=BC, not AB=BC.

Jobayer Mahmud - 6 years, 10 months ago

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hey, thanks for pointing out th mistake

Arun AR - 6 years, 10 months ago

AD and ST are the diameters of the circle with center O. AB is chord of the circle. OC perpendicular to AB means it bisects AB. therefore, AC= BC= 4m

OC parallel BD and OC perpendicular to AB means triangle CBD is a right angled triangle right angled at B, area of triangle CBD is given and we get BD= 6m.

ABD is a right angled triangle right angled at B, we get AD=10m

using Pythagoras theorem AD = ST = 10m OS =OT = OA = OD =5m

triangle ACO is a right angled triangle right angled at C, using Pythagoras theorem OC= 3m

CS= OS + OC = 5 + 3 = 8m

Arun AR - 6 years, 10 months ago
Khushwant Singh
Mar 31, 2015

since OC bisects AB, therefore AC=BC=4m. now the area of triangle BCD is given and BC=4, so we can get BD=6. Now, since OC||BD and O and C are mid-points of AD andAB respectively, we can use MID POINT THEOREM and can get OC=1/2BD=3. Now we have AC and OC, we can find AO=5( radius) by Pythagoras theorem . Finally CS= OS +OC=5+3=8

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