Question

A chord of ⦿ (O, 5) touches ⦿ (O, 3). Therefore the length of the chord = ......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 8
(b) 10
(c) 7
(d) 6

Answer 1

R = 5 , r = 3 are radii of Concentric circles.

PB = √ R² - r²

= √5² - 3²

= √ 25 - 9

= √16

PB = 4

Therefore ,

Chord = AB

= 2 × PB

= 2 × 4

= 8

Therefore ,

option ( a ) is correct.

I hope this helps you.

: )

Answer 2

Let OP and OA is the radius of circle.

First see figure which is attached.

Now, apply Pythagoras theorem in ΔAOP

$OP^{2} +AP^{2} =OA^{2}$

$3^{2} +AP^{2} =5^{2}$

$AP^{2} =5^{2} -3^{2}$

$AP^{2} =16$

$AP=\sqrt{16}$

$AP = 4$

AP= PB

Hence, length of chord is 2AP = 8.

Option A is correct.