Question

a chord of a circle is equal to the radius of the circle find find the angle subtended by the chord at a point on the minor Arc and also at a point on the maker arc​

Answer 1

Answer:Given,

AB is equal to the radius of the circle.

In △OAB,

OA=OB=AB= radius of the circle.

Thus, △OAB is an equilateral triangle.

∠AOC=60°

Also, ∠ACB=  

2

1

​  

∠AOB=  

2

1

​  

×60°=30°

ACBD is a cyclic quadrilateral,

∠ACB+∠ADB=180° ∣ Opposite angles of cyclic quadrilateral

⇒∠ADB=180°−30°=150°

Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30° respectively.

Step-by-step explanation:

Answer 2

Answer:

Given,

AB is equal to the radius of the circle.

In △OAB,

OA=OB=AB= radius of the circle.

Thus, △OAB is an equilateral triangle.

∠AOC=60°

Also, ∠ACB=

2

1

∠AOB=

2

1

×60°=30°

ACBD is a cyclic quadrilateral,

∠ACB+∠ADB=180° ∣ Opposite angles of cyclic quadrilateral

⇒∠ADB=180°−30°=150°

Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30° respectively.

Step-by-step explanation:

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