Question

radius of a circle is 34cm and the distance of the chord from the center is 30cm. find the length of the chord​

Answer 1

$\large\underline\mathfrak\red{Given \: :- }$

• Radius of circle (OA) = 34cm
• Distance to the chord from the centre (OC) = 30cm

$\large\underline\mathfrak\red{To find \: :- }$

• Length of chord

$\large\underline\mathfrak\red{Solution \: :- }$

We know that,

Radius of circle (OA) = 34cm

Distance to the chord from the centre (OC) = 30cm

Let's learn about Pythagoras's theorem :

In mathematics, the Pythagorean theorem, or Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

______________________________

Taking Pythagoras's theorem to solve this question

$\large\underline\mathfrak\green{Pythagoras's \: formula \: : }$

${\large{\underline{\boxed{\sf{Hypotenuse² = Height² + Base² }}}}}</p><p></p><p>$

Here,

Hypotenuse = OA = 34 cm

Height OC = 30 cm

Base AC = Find ?

Required answer

$\sf\implies{OA² = OC² + AC² }$

$\sf\implies{34² = 30² + AC² }$

$\sf\implies{1156 = 900 + AC² }$

$\sf\implies{AC² = 1156 - 900 = 256}$

$\sf\implies{AC² = 256}$

$\sf\implies{AC = \sqrt{256} = 16}$

Base = AC = 16 cm

We have to find Chord means AB

$\sf{AB = 2AC}$

Finding Chord

$\sf\implies{AB = 2×16=32cm}$

${\large{\underline{\boxed{\sf{\red{Chord = 32cm }}}}}}$

_____________________________________