# NCERT Class 9 Solutions: Circles (Chapter 10) Exercise 10.4 – Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q-1 Two circles of radii and intersect at two points and the distance between their centres is . Find the length of the common chord.

Solution:

Given, two circles with radius and .

- , and .
- Also (as we proved above)
- Let be .

In ,

- … equation (1)

In ,

- … equation (2)

Equating (1) and (2) ,

Putting the value of in (1) we get,

Therefore, length of the chord

Q-2 If two equal chords of a circle intersect within the circle; prove that the segments of one chord are equal to corresponding segments of the other chord.

Solution:

- Given, PQ and SR are chords intersecting at T and
- To prove, And

Construction, draw perpendicular bisectors of PQ and SR. Line from the center which bisects a chord is perpendicular to the chord.

- bisects
- bisects

As

- … equation (1)
- Because M and N are midpoints of PQ and SR, … equation (2)

In and

- (perpendiculars)
- (common line)
- ( and thus equidistant from the centre)
- By Right Angle Hypotenuse congruence condition.
- by Corresponding Parts of Congruent Triangles … equation (3)

From (1) and (2) we get,

- (since we are adding equal parts (MT and TN) to equal quantities what we get according to Euclid is also equal)
- Therefore,

Again,

- (since we are subtracting equal parts (MT and TN) from equal quantities what is left according to Euclid is also equal)