Question

AB is minor arc in a circle with centre P. R is the point on the major arc except A and B. If angleAPB = 150, then angle ARB = (A) 150 (B) 75 (C) 50 (D) 100 ​

Answer 1

Answer:

Consider the figure.

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.

and ∠AOC=60°.

Also, ∠ACB=

2

1

∠AOB=

2

1

×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.