Q2 of 31 Page 65

The length of a diameter of a circle with its centre at O is 26 cm. The distance of the chord PQ from the point O is 5 cm. Let us write by calculating, the length of the chord PQ.



Given Length of the diameter = 26cm, Distance of Chord PQ From center = 5cm


Radius


Radius = 13cm


In O PD , Using Pythagoras Theorem


Hypotenuse2 = base2 + Height2


⇒ OP2 = OD2 + PD2


⇒ 132 = 52 + PD2


⇒ PD2 = 169-25


⇒ PD2 = 144


⇒ PD = 12cm


⇒ PQ = 2 PD


⇒ PQ = 24cm


More from this chapter

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4

Let us write true or false:

i. The circle is a plane figure.


ii. The segment is a plane region.


iii. The Sector is a plane region.


iv. The chord is a line segment


v. The arc is a line segment.


vi. There are finite number of chords of same length in a circle


vii. One and only one circle can be drawn by taking a fixed point as its centre.


viii. The lengths of the radii of two congruent circles are equal.

 1

The length of a radius of a circle with its centre O is 5 cm. and the length of its chord AB is 8 cm. Let us write by calculating, the distance of the chord AB from the centre O.

 3

The length of a chord PQ of a circle with its centre O is 4 cm. and the distance of PQ from the point O is 2.1 cm. Let us write by calculating, the length of its diameter.

 4

The lengths of two chords of a circle with its centre O are 6 cm. and 8 cm. If the distance of smaller chord from centre is 4 cm, then let us write by calculating, the distance of other chord from the centre.