Question

The parallel chord lie on opposite sides of the center of a circle of a circle of radius 13cm.their lengths are 10cm and 24cm respectively. What is the Distance between the chords

Answer 1

Answer:

Distance between both parallel chords will be 17cm...

Step-by-step explanation:

Given

---The parallel chords lie on opposite side of the center of a cirlce.

---The radius of a circle is of length 13cm.

---And the lengths of parallel chords are 10cm and 24cm respectively.

Now ,

Let the parallel chords be AB and CD respectively with center lie on point O.

To Find

Distance between chords..

Construction--

Join BC and CD both lines passes through center O.

Draw a line PQ such that it passes through center O and bisect both Chords ..

Now using Pythagoras Theorem :

We can determine OP and OQ

1.OP

In right triangle ∆OCP , right angle at P

OC^2 = OP^2 + PC^2. {•OC =13cm (Radius)

•PC = 5cm (half of

chord CD)}

now,

169 = OP^2 + 100

OP^2 = 144

OP = 12cm

2.OQ

Now in right triangle OQS:

OA^2 = QA^2 + OQ^2

Same as previous triangle

169= 144 + OQ^2

OQ^2 = 25

OQ = 5 cm

Now Distance between Parallel chords = OP+OQ

= 12 + 5

= 17 cm