Question

two concentric circles are of radii 6.5 cm and 2.5 cm . find the length of the cord of the larger circle which touches the smaller circle​

Answer 1

Step-by-step explanation:

We know that the radius and tangent are perpendicular at their point of contact In right triangle AOP Since, the perpendicular drawn from the center bisects the chord. PA = PB = 6 cm Now, AB = AP + PB = 6 + 6 = 12 cm Hence, the length of the chord of the larger circle is 12 cm.Read more on Sarthaks.com - https://www.sarthaks.com/157193/concentric-circles-radii-find-length-chord-larger-circle-which-touches-the-smaller-circle

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Answer 2

Step-by-step explanation:

Let O be the center of circle. Draw two concentric circles are of radii 6.5cm and 2.5cm, and

$$AB =$$ Chord of the larger circle which touches the smaller circle at C.

From Figure:

OC= radius =2.5cm

OA=6.5cm

AC=CB

OC⊥AB and OC bisects AB at C.

In right ΔOPT,

By Pythagoras Theorem:

OA

2

=OC

2

+AC

2

6.5

2

=2.5

2

+AC

2

42.25=6.25+AC

2

AC=6

Length of chord of a circle =AB=2×AC=2×6=12cm.