Question

The figure shows two concentric circles, C, (radius 5 cm) and C (radius 3 cm).
Chord AB tangent is to circle C, at C. What is the length of chord AB?​

Answer 1

Answer:

Let two circles have the same centre O and AB is a chord of the larger circle touching the smaller circle at C.

OA=5cm and OC=3cm

Now,

As we know that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Therefore,

In △OAC,

OA

2

=OC

2

+AC

2

(By pythagoras theorem)

⇒AC

2

=OA

2

−OC

2

⇒AC

2

=(5)

2

−(3)

2

⇒AC=

25−9

=

16

=4cm

Since perpendicular drawn from the centre of circle bisects the chord.

Therefore,

AB=2AC

⇒AB=2×4=8cm

Hence the length of the chord is 8cm.

Step-by-step explanation:

hope it helps

Answer 2

in Greek the Pythagorean in Greek followers of the famous mathematician and philosopher Pythagoras where the first to discover the number which were not reasonal around 400 BCo