Question

1. Two parallel chords of a circle whose diameter Is 13cm are respectively 5cm and 12cm .find the distance between them if they lie on opposite sides of center.

Answer 1

Draw a perpendicular from the centre (O) of the circle to the chords AB and CD. The perpendicular bisects the chords at P and Q respectively.

OP2 + PB2 = OB2

OQ2 + QD2 = OD2

Subtracting second equation from the first

OP2 - OQ2 + PB2 - QD2 = OB2 - OD2

(OP - OQ)(OP + OQ) = 62 - 2.52 = (6 - 2.5)(6 + 2.5)

OE - OF = 3.5 cm

I have also attached another method. Please do see to that too :)

Hope This Helps :)

Answer 2

Question:

Two parallel chords of a circle whose diameter Is 13cm are respectively 5cm and 12cm .find the distance between them if they lie on opposite sides of center.

Step-by-step explanation:

Let the distance from chords of 5 cm to the centre of the circle and the distance from chords of 12 cm to the center of the circle be A and B respectively.

Given,

Diameter of circle = 13 cm

Radius of circle = 6.5 cm

Half of chord = 5/2 = 2.5 cm

Half of other chord = 12/2 = 6 cm

Using Pythagoras theorem for 5 cm chord,

⇒ 6.52 = 2.52 + A2

⇒ A2 = 36

⇒ A = 6 cm

Using Pythagoras theorem for 12 cm chord,

⇒ 6.52 = 62 + B2

⇒ B2 = 6.25

⇒ B = 2.5 cm

Distance between two chords when they are in semicircle

= 6 – 2.5 = 3.5 cm

The final answer is 3.5cm.

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