Name: Theorems Related to Chords and Subtended Angle
Uploaded: 2019-07-19
Duration: 32 min 30 s
Description: In this video, we will study the theorem on equal chords that are equidistant from the origin and proof, examples and constructions etc, in detail.

Question

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

Accepted Answer

A circle is a collection of points which are equidistant from a fixed point known as the centre of the circle and this equal distance is called as radius of circle.

Now, if we try to superimpose two circles of equal radius on each other, then both circles will cover each other.

So, two circles are congruent if they have equal radii.

Now consider two congruent circles having centre $O$ and $O'$ and two chords $A B$ and $C D$ of equal length.

Now, in $△ A O B$ and $△ C O' D$

$A B = C D$ ( $∵$ Chords of same length)

$O A = O' C$ ( $∵$ Radii of congruent circles)

$O B = O' D$ ( $∵$ Radii of congruent circles)

$∴ △ A O B ≅ △ C O' D$ (By $S S S$ congruency)

$\Rightarrow ∠ A O B = ∠ C O' D$ (Corresponding angles of congruent triangles)

Hence, equal chords of congruent circles subtend equal angles at their centres.

Madhya Pradesh Board Solutions for Chapter: Circles, Exercise 2: EXERCISE

Madhya Pradesh Board Mathematics Solutions for Exercise - Madhya Pradesh Board Solutions for Chapter: Circles, Exercise 2: EXERCISE

Questions from Madhya Pradesh Board Solutions for Chapter: Circles, Exercise 2: EXERCISE with Hints & Solutions

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