Question

The length of a chord 78cm long is 52cm away from the centre. What is the length of another chord which is 60cm away from the centre
5 points

Answer 1

Answer:

If a chord 52 cm away from the centre of the circle is 78cm long how long is the 60 cm away from the centre?

The chord is bisected by the perpendicular from the center. Let the perpendicular from the center O meets the chord AB at C .

In triangle AOC, <C=90 . AO = radius , AC=1/2 AB = 78/2 =39cm

OC =distance of the chord from the center = 52 cm

In ∆AOC,

AO^2= OC^2+AC^2

AO^2 = 52^2 +39^2

AO= 65cm.

Let the other chord be PQ which is 60 cm away from the center O.

Let OR = 60 .

In ∆POR ,

PO ^2= PR^2+OR^2

PR^2= PO^2-OR^2

=65^2–60^2 = 625

PR=25 cm.

Length of the chord PQ=2PR=50 cm.