MCQ
Write the correct answer in the following: In Fig. if $\angle\text{OAB}=40^\circ,$ then $\angle\text{ACB}$ is equal to: 
- ✓$50^\circ .$
- B$40^\circ .$
- C$60^\circ .$
- D$70^\circ .$
✓
Answer
Correct option: A.
$50^\circ .$
In $\triangle\text{QAB, OA} = \text{OB}$ [both are the radius of a circle]
$\angle\text{OAB} = \angle\text{OBA}\Rightarrow \angle\text{OBA} = 40^\circ$
[angles opposite to equal sides are equal]
Also, $\angle\text{AOB} = \angle\text{OBA}\Rightarrow \angle\text{BAO} = 180^\circ$
[by angle sum property of a triangle]
$\angle\text{AOB} + 40^\circ + 40^\circ = 180^\circ$
$\Rightarrow\ \angle\text{AOB} = 180^\circ – 80^\circ = 100^\circ$
We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
$\angle\text{AOB} = 2 \angle\text{ACB} \Rightarrow 100^\circ =2 \angle\text{ACB}$
$\angle\text{ACB} = \frac{100}{2} = 50^\circ$
$\angle\text{OAB} = \angle\text{OBA}\Rightarrow \angle\text{OBA} = 40^\circ$
[angles opposite to equal sides are equal]
Also, $\angle\text{AOB} = \angle\text{OBA}\Rightarrow \angle\text{BAO} = 180^\circ$
[by angle sum property of a triangle]
$\angle\text{AOB} + 40^\circ + 40^\circ = 180^\circ$
$\Rightarrow\ \angle\text{AOB} = 180^\circ – 80^\circ = 100^\circ$
We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.
$\angle\text{AOB} = 2 \angle\text{ACB} \Rightarrow 100^\circ =2 \angle\text{ACB}$
$\angle\text{ACB} = \frac{100}{2} = 50^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The point of the form $(\text{a},\ \text{a}),\ \text{a}\neq0$ lies on:
→The value of $0 . \overline{2} \times 0 . \overline{5}$ is
→$AD$ is diameter of a circle, $O$ being the centre and $AB$ is a chord. Let the centre of $AB$ be denoted by $M,$ then find $OM.$
→The side $BC, CA$ and $AB$ of $\triangle\text{ABC}$ have been produced to $D, E$ and $F$ respectively. $\angle\text{BAE}+\angle\text{CBF}+\angle\text{ACD}=?$
→Two circular cylinders of equal volume have their heights in the ratio $1 : 2.$ The ratio of their radii is:
→In Fig. if $l_1 \| l_2$ and $l_3 \| l_4$ what is y in terms of x?
→In the given figure, $AB > AC.$ Then which of the following is true$?$
→In $\triangle A B C, \angle A=30^{\circ}, \angle B=40^{\circ}$ and $\angle C=110^{\circ}$. The angles of the triangle formed by joining the mid-points of the sides of this triangle are
→Two complementary angles are such that twice the measure of the one is equal to three times the measure of the other. The larger of the two measures.
The area of the triangle formed by the point P (-3, 4) and its reflections in the coordinate axes is