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RD Chapter 16 Circles Ex 16.4 Solutions

Question - 11 : - 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 arc and also at a point on the major arc.

Answer - 11 : -

We have to find   and  
 
Construction: - O is centre and r is radius and given that chord is equal to radius of circle
Now in   we have

AO = OB = BA       ( It is given that chord is equal to radius of circle)
So,   is an equilateral triangle
So, ∠AOB=2∠ADB∠AOB=2∠ADB                (The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle)
Then  
So
 Therefore,
  and  

Hence, the angle subtended by the chord at a point on the minor arc is 150° and also at a point on the major arc is 30°.

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