Question

in the given figure radius of circle is 5 cm.chords AB and CD are parallel and distance between them is 7 cm.if CD=6 cm,find AB

Answer 1

Answer :

[Figure in the attachment]

Given -

• Two chords AB and CD are parallel to each other.
• The Radius = 5 cm.
• The length of chord CD = 6 cm.
• The Distance between the chords = 7 cm.

To Find -

• Length of chord AB ?

Solution -

We know that, CD = 6 cm.

Hence, ½CD = 3 cm.

Now, PC = 3 cm and OC = 5 cm.

Using Pythagoras theorem in ∆PCO :

➜ OC² = PC² + OP²

➜ 5² = 3² + OP²

➜ 25 - 9 = OP²

➜ OP = √16

➜ OP = 4 cm.

Now, We know that PQ = 7 cm.

So, OQ = 7 - 4 = 3 cm.

Using Pythagoras theorem in ∆QAO :

➜ OA² = QA² + OQ²

➜ 5² = QA² + 3²

➜ 25 - 9 = QA²

➜ QA = √16

➜ QA = 4 cm.

Now, 2×QA = 2×4 = 8 cm.

Hence, AB = 8 cm.

Answer 2

Answer:

8cm

See figure above, Hope it helps!!