Calculate the length of a chord which is at a perpendicular distance o

1.	Calculate the length of a chord which is at a perpendicular distance of5 cm from the centre of a circle of radius 13 cm.
Answer» ⇒ Final Answer: 28 cm ⇒ Given: Perpendicular distance from the chord to the centre of the circle = 5 cm Radius of the circle = 13 cm Please REFER the attachment for pictorial representation. ⇒ To Find: The length of the chord. ⇒ Solution: In the diagram: AD = 13 cm DC = 5 cm It is given that: the perpendicular distance from the chord to the centre of the earth is 5 cm. This means that, ΔACD is right angled. Now, applying the Pythagoras THEOREM, Altitude² + Base² = Hypotenuse² AD² + DC² = AC² 13² + 5² = AC² 169 + 25 = AC² 196 = AC² AC = √196 AC = 14 cm As AC is the half of the complete chord AB, the measure the complete chord = 2 x 14 = 28 cm Hence the required answer is 28 cm. Knowledge Bytes: → IMPORTANT terms used in the answer: ✳ Chord A chord is a line SEGMENT that connects two points in the boundary of the circle. The longest chord in a circle is the diameter. ✳ Radius The radius is the short line segment that connects the center of the circle to any point in the boundary of the circle. A diameter is 2 x radius. The measure of a radius of a circle is always the same.

Calculate the length of a chord which is at a perpendicular distance of5 cm from the centre of a circle of radius 13 cm.

Answer»

⇒ Final Answer:

28 cm

⇒ Given:

Perpendicular distance from the chord to the centre of the circle = 5 cm

Radius of the circle = 13 cm

Please REFER the attachment for pictorial representation.

⇒ To Find:

The length of the chord.

⇒ Solution:

In the diagram:

AD = 13 cm

DC = 5 cm

It is given that:

the perpendicular distance from the chord to the centre of the earth is 5 cm.

This means that, ΔACD is right angled.

Now, applying the Pythagoras THEOREM,

Altitude² + Base² = Hypotenuse²

AD² + DC² = AC²

13² + 5² = AC²

169 + 25 = AC²

196 = AC²

AC = √196

AC = 14 cm

As AC is the half of the complete chord AB, the measure the complete chord

= 2 x 14

= 28 cm

Hence the required answer is 28 cm.

Knowledge Bytes:

→ IMPORTANT terms used in the answer:

✳ Chord

A chord is a line SEGMENT that connects two points in the boundary of the circle. The longest chord in a circle is the diameter.

✳ Radius

The radius is the short line segment that connects the center of the circle to any point in the boundary of the circle. A diameter is 2 x radius. The measure of a radius of a circle is always the same.