Question

the distance of chord PQ from the center of circle is 5cm length of the chord PQ is 24cm.then find the radius of circle​

Answer 1

Given:-

• Distance of chord from centre ,RO = 5 cm
• Length of Chord ,PQ = 24 cm

To Find:-

• Radius of the Circle ,PO

Solution:-

⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

As we know that shortest distance between centre of circle and a chord is the perpendicular bisector of the chord

$\mathtt{:\implies PQ = 2PR = 24 }\\ \\ \mathtt{:\implies PR = 24/2 = 12 cm}$

Now, calculating the length of radius of the circle. Using Pythagoras Theorem .

:⟹ PO² = PR² + OR²

substitute the value we get

⠀⠀:⟹ PO² = 12² + 5²

⠀⠀⠀⠀:⟹ PO² = 144 + 25

⠀⠀⠀⠀⠀:⟹ PO² = 169

⠀⠀⠀⠀⠀⠀⠀:⟹ PO = √ 169

⠀⠀⠀⠀⠀⠀⠀⠀:⟹ PO = 13

Hence the length of the radius is 13 cm .