Prove that equal chords of congruent circles | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(N/A) Let there be two congruent circles with centres $O$ and $O'$.Let $AB$ be a chord of the first circle and $CD$ be a chord of the second circle su

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) Let there be two congruent circles with centres $O$ and $O'$.
Let $AB$ be a chord of the first circle and $CD$ be a chord of the second circle such that $AB = CD$.
We need to prove that $\angle AOB = \angle CO'D$.
In $\triangle AOB$ and $\triangle CO'D$:
$1. OA = O'C$ (Radii of congruent circles are equal).
$2. OB = O'D$ (Radii of congruent circles are equal).
$3. AB = CD$ (Given).
By $SSS$ (Side-Side-Side) congruence criterion,$\triangle AOB \cong \triangle CO'D$.
Since the triangles are congruent,their corresponding parts are equal $(CPCT)$.
Therefore,$\angle AOB = \angle CO'D$.

Prove that equal chords of congruent circles subtend equal angles at their centres.

Similar Questions

If $BM$ and $CN$ are the altitudes drawn on the sides $AC$ and $AB$ of the triangle $ABC$,prove that the points $B, C, M$ and $N$ are concyclic.

There is one and only one circle passing through all the vertices $A, B$ and $C$ of $\Delta ABC$. This circle is called the ............. of $\Delta ABC$.

$ABCD$ is a cyclic quadrilateral such that $AB$ is a diameter of the circle circumscribing it and $\angle ADC = 140^{\circ}$,then $\angle BAC$ is equal to (in $^{\circ}$)

In the figure,if $\angle ABC = 20^{\circ},$ then $\angle AOC$ is equal to (in $^{\circ}$)

In a cyclic quadrilateral $ABCD$,diagonals $AC$ and $BD$ intersect at $P$. If $\angle BAC = 52^{\circ}$ and $\angle ADB = 78^{\circ}$,then find $\angle ABC$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module