Question

Length of a chord is 1cm away from the centre of a circle is 6cm what is the radius of the circle​

Answer 1

Answer:

The first chord is 1 cm away from the centre and 6cm long, so drawing in a radius creates a right-angled triangle with sides 1 and 3 and tells us by Pythagoras that the radius must be 10−−√10 cm

Now we do the same thing for the second chord. This time, it’s the chord length that’s unknown, but the radius is the same. By Pythagoras again, the length of half the chord is 10−4−−−−−√10−4 , so the whole chord has a length of 26–√26 cm

Step-by-step explanation:

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Answer 2

Given :- Length of a chord is 1cm away from the centre of a circle is 6cm .

To Find :- The radius of the circle = ?

Concept used :-

• A line drawn from the centre of a circle to a chord always bisects it at 90° .

Solution :-

given that,

→ Length of chord = 6 cm

So,

→ Half of chord = 6/2 = 3 cm

and,

→ Distance from centre = 1 cm .

Let us assume that radius of given circle is r cm .

since line from centre bisect the chord at right angle .

In right angled ∆ we have,

→ Radius = √[(Half of chord)² + (Distance from centre)²] { By pythagoras theorem }

→ r = √(3² + 1²)

→ r = √(9 + 1)

→ r = √10 cm (Ans.)

Hence, radius of circle is equal to √10 cm .

Solution with Image :-

→ O = Centre of circle .

→ OA = Radius of circle .

→ OC = Distance from centre = 1 cm

→ AB = chord = 6 cm

So,

→ AC = 6/2 = 3 cm

now, in right angled ∆OCA,

→ OA = √(OC² + AC²) { By pythagoras theorem }

→ OA = √(3² + 1²)

→ OA = √(9 + 1)

→ OA = √10 cm (Ans.)

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