Question

length of a chord ofva circle is 24cm . if distance of the chord from the center is 5cm ,then the radius of that circle is _____​

Answer 1

Given:

• Length of a chord (SJ) = 24 cm
• Distance of the chord from the center (RA) = 5 cm

To Find:

• The radius of that circle.

Diagram:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(-1.9,-1.3){\line(1,0){3.85}}\qbezier(1.95,-1.3)(1.95,-1.3)(0,0.2)\put(0,0.2){\line(0,-1){1.5}}\put(-0.1,0.5){\bf R}\put(-2.5,-1.5){\bf S}\put(2.3,-1.5){\bf Y}\put(-0.15,-1.75){\bf A}\put(-1.9,-2.7){\vector(1,0){3.85}}\put(-1.9,-2.7){\vector(-1,0){0}}\put(-0.5,-3.2){\bf 24\ cm}\put(-1.2,-0.63){\bf 5\ cm}\end{picture}$

Solution:

Draw, RA ⊥ SJ

We know that,

Perpendicular drawn from centre of a circle to a chord bisects the chord.

⇒ SA = AJ = ¹/2 × SJ

⇒ SA = AJ = ¹/2 × 24

⇒ SA = AJ = 12 cm

In ΔRAJ, m∠ABC = 90°

According to the pythagorus theorem,

⇒ RJ² = RA² + AJ²

⇒ RJ² = 5² + 12²

⇒ RJ² = 25 + 144

⇒ RJ² = 169

⇒ RJ = 13 cm

Hence,

The radius of that circle is 13 cm.