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