Algebra.Com's Answer #695968 by ikleyn(52790)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "The points A and C lie on a circle with center O and radius 5 sq.root of 2. The point within the circle is such that ABC = 90 degrees.
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document.write( "Following the data: AB = 6, BC = 2, Find OB.
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document.write( "It seems this problem is slightly above the average school geometry level.
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document.write( "So, I will assume that your level corresponds to that.
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document.write( "Therefore, I will give you only general instructions/directions, leaving calculations and details to you.\r
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document.write( "0. Make a sketch to follow my arguments.\r\n" );
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document.write( " You have the circle of the radius  with the center at the point O.\r\n" );
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document.write( " You have the right-angled triangle ABC leaning on the chord AC.\r\n" );
document.write( " The legs AB and BC are of the lengths 6 and 2 units.\r\n" );
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document.write( "1. Hence, the length of the chord AC (which is the hypotenuse) is\r\n" );
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document.write( " |AC| =  =  .\r\n" );
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document.write( "2. The distance from the center O to the chord AC is  =  =  = .\r\n" );
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document.write( " It is the length of the perpendicular OD drown from the center O to the mid-point D of the chord AC.\r\n" );
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document.write( "3. Draw the altitude BE in the right angled triangle ABC from the right angle vertex to the hypotenuse AC.\r\n" );
document.write( " (E is the base of this altitude).\r\n" );
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document.write( " You can find the length of BE from the \"AREA\" equation of the triangle ABC:\r\n" );
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document.write( "  =  , ====> |BE| =  .\r\n" );
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document.write( "4. Now you can calculate one component of the segment OB.\r\n" );
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document.write( " (I call this component \"vertical\" component of the segment OB, since it is vertical component in my sketch . . . )\r\n" );
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document.write( " This vertical component is |OD| - |BE| =  .\r\n" );
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document.write( "5. Next step is to find the horizontal component of the segment OB.\r\n" );
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document.write( " For it, you need to determine in which segments the altitude DE divide the hypotenuse AC.\r\n" );
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document.write( " It is very standard task (sub-task), and every advanced student must be able to do it.\r\n" );
document.write( " (Use similarity of right-angled triangles).\r\n" );
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document.write( " When you complete this sub-task, you will get the horizontal component of the segment OB by subtracting half of the chord AC length.\r\n" );
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document.write( "6. Having the horizontal and the vertical components of OB, you will be in position to find its length.\r\n" );
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