# The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the centre, what is the distance of the other chord from the centre?

**Solution:**

The perpendicular drawn from the center of the circle to the chords bisects it.

Draw two parallel chords AB and CD of lengths 6 cm and 8 cm. Let the circle's center be O. Join one end of each chord to the center. Draw 2 perpendiculars OM and ON to AB and CD, respectively, which bisects the chords.

AB = 6 cm CD = 8 cm MB = 3 cm ND = 4 cm

Given OM = 4 cm and let ON = x cm Consider ΔOMB

By Pythagoras theorem,

OM² + MB² = OB²

4² + 3² = OB²

OB² = 25

OB = 5 cm

OB and OD are the radii of the circle.

Therefore OD = OB = 5 cm.

Consider ΔOND

ON² + ND² = OD²

x² + 4² = 5²

x² = 25 - 16

x² = 9

x = 3

The distance of the chord CD from the center is 3 cm.

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 10

**Video Solution:**

## The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at distance 4 cm from the center, what is the distance of the other chord from the centre?

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.6 Question 3

**Summary:**

The lengths of two parallel chords of a circle are 6 cm and 8 cm. If the smaller chord is at a distance of 4 cm from the center, we have found that the distance of the other chord CD from the center is 3 cm.

**☛ Related Questions:**

- Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the center.
- Prove that the circle drawn with any side of a rhombus as diameter, passes through the point of intersection of its diagonals.
- ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Prove that AE = AD.
- AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are diameters, (ii) ABCD is a rectangle.

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