Question

in the figure o is the centre of the circle if angle OAB=40 and C is a point inside the Circle then find angle ACB

please answer!!

THANX!

Answer 1

Angle ACB is 100 because sum angles in triangle is 180 in the given one side is 40 other is also 40 so it is 100

Answer 2

Given:

∠$OAB$ = $40$°

To  find:

∠$ACB$ = ?

Solution:

We can see that, in ΔOAB,

OA = OB  ; since they are the radius of circle.

Also, we know that angles opposite to equal sides of a triangle are also equal.

Hence,

∠OAB = ∠OBA = 40°  

Now, in ΔOAB , we have

∠OAB + ∠OBA + ∠AOB = 180°

40° + 40° + ∠AOB = 180°

Therefore, ∠AOB = 100°

Now, we know that

• If on a chord, there are two angles, one directed towards the center and other towards the circumference of the circle, then, the angle made on the center of circle is double than than made on the circumference.

Mathematically,

∠AOB = 2 × ∠ACB

Substituting the given values, we get

∠ACB = 50°

Final answer:

Hence, the ∠ACB = 50°.