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Question

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor are and also at a point on the major are.


Solution

A circle with centre O, a chord AB =  radius of the circle C and D are points on the minor and major arcs of the circle

ACB and ADB are formed

Now in ΔAOB,

OA = OB = AB       ( AB = radii of the circle)

 ΔAOB is an equilateral triangle,

AOB=60

Now are AB subtends AOB at the centre and ADB at the remainder part of the circle.

ADB=12AOB=12×60=30

Now ACBD is a cyclic quadrilateral,

ADB+AOB=12×60=30

Now ACBD is a cyclic quadrilateral,

ADB=12AOB=12×60=30

Now ACBD is a cyclic quadrilateral,

 ADB+ACB=180

(Sum of opposite angles of the cyclic quad.)

30+ACB=180

ACB=180

ACB=18030=150

ACB=150

Hence angles are 150, and 30

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