a chord of a circle is equal to the radius of the circle find the angle subtended by the chord at the point of the minor arc
Answers
Answer:
AB is equal to the radius of the circle.
In △OAB,
OA=OB=AB= radius of the circle.
Thus, △OAB is an equilateral triangle.
and ∠AOC=60°.
Also, ∠ACB=21∠AOB=21×60°=30°.
Since, ACBD is a cyclic quadrilateral,
∠ACB+∠ADB=180° ....[Opposite angles of cyclic quadrilateral are supplementary]
⇒∠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.
AB is equal to the radius of the circle.
In △OAB,
OA=OB=AB= radius of the circle.
Thus, △OAB is an equilateral triangle.
and ∠AOC=60°.
Also, ∠ACB=21∠AOB=21×60°=30°.
Since, ACBD is a cyclic quadrilateral,
∠ACB+∠ADB=180° ....[Opposite angles of cyclic quadrilateral are supplementary]
⇒∠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.