Question

In the given figure, O is the centre of the circle and AB is the diameter. If ∠ = 90 and OB =
◦
BC, find ∠1.
a) 30
o
b) 45
o
c) 60
o
d) 70
o

Answer 1

Answer: The measure of ∠1 = 60° , hence answer is c) 60°

Step-by-step explanation:

Given Data:

O is the centre of the circle,

AB is the diameter.

OB = BC

∠C = 90° (assume since not given in question, also we know that diameter subtends 90° angle on any point of the circle.)

To find: ∠1

Refer the attached image (some parts are assumed since detail not mentioned)

Now, in the given circle, OA = OB = OC (since they are radii)

Also, OB = BC (given)

So, in ΔBOC, 0B = BC= OC

⇒ΔBOC is equilateral triangle.   (all sides equal)

Therefore all the angles, measure = 60°

Hence ∠1 = 60° (assuming it is one of the angles of ΔBOC, since figure not given)