Question
Two congruent circles with centres $O$ and $O′$ intersect at two points $A$ and $B.$ Then $\angle\text{AOB}=\angle\text{AO'B}.$
✓
Answer
Join $AB$ and $OB, O'A$ and $BO'.$
In $\triangle\text{AOB}$ and $\triangle\text{AO'B,} OA = AO' [$both circles have same radius$] OB = BO' [$both circles have same radius$]$ and $AB = AB [$common chord$]$
$\triangle\text{AOB}=\triangle\text{AO'B} [$by $SSC$ congruence rule$]$
$\Rightarrow\angle\text{AOB}=\angle\text{AO'B}[ $by $CPCT]$
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
If $AOB$ is a diameter of a circle and $C$ is a point on the circle, then $\mathrm{AC}^2+\mathrm{BC}^2=A B^2$.
→ The following statements are true and which are false?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.
Write whether the following statements are True or False$?$ Justify your answer. Points $(1, -1)$ and $(-1, 1)$ lie in the same quadrant.
→Write whether the following statements are True or False? Justify your answer: Two distinct intersecting lines cannot be parallel to the same line.
The following statements are true $(T)$ and which are false $(F):$ If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
→State whether the given statement is true of false. The product of two rational numbers is rational.
The following statements are true and which are false? Sum of any two sides of a triangle is greater than twice the median drown to the third side.
Write whether the following statements are True or False$?$ Justify your answer. Point $(3, 0)$ lies in the first quadrant.
→ Line segment joining the center to any point on the circle is a radius of the circle,