Question

please anyone give me easiest solution of this question please
And a very happy rose day to all my besties.

Answer 1

Answer:

20√3 m

Step-by-step explanation:

Let the three boys are sitting at A,B,C on the circular path. As three boys are sitting at equal distances from each other, ABC is an equilateral triangle.

⇒ OA = r = 20 m.

From figure:

AD is a median and it passes through the centre O of the circle. Also, O is the centroid of ΔABC,

⇒ OA = (2/3)AD     ---- (i)

Let the side of ΔABC be 'x' metres. Then,

⇒ BD = (x/2) metres.

⇒ AB = x m.

In ΔABD,

⇒ (AB)² = (BD)² + (AD)²

⇒ x² = (x/2)² + (AD)²

⇒ x² - (x/2)² = (AD)²

⇒ (4x² - x²)/4 = (AD)²

⇒ 3x²/4 = (AD)²

⇒ (√3/2)x =AD

Substitute AD in (i), we get

⇒ OA = (2/3) * AD

⇒ OA = (2/3) * (√3/2) * x

⇒ 20 = (√3/3) x

⇒ x = 20√3 m.

Therefore, Length of the string of each phone is 20√3 m.

Hope it helps!

Answer 2

Answer : 20√3.

Step-by-step explanation :

Here, arc(AB) = arc(BC) = arc(AC)

Since chords corresponding to equal arcs are also equal therefore,

Chord(AB) = Chord(BC) = Chord(AC)

Hence, AB = BC = AC

Thus, ABC is none other than a equilateral ∆.

We know that when an equilateral ∆ is inscribed within circle then its Centroid is only the circum center.

So, we have medians BE, CF and AD meeting at G ( Centroid ) which is center of circle.

When any line that falls from center bisecting in the chord then the line is perpendicular bisector.

Now, medians in an equilateral traingle are equal so,

AD = CF = BE

⅔ AD = ⅔ CF = ⅔ BE

AG = CG = BG

Where AG = 20 m

So, AG = ⅔ AD

20 m = ⅔ AD

30 m = AD

So, GD = AD - AG

GD = 30 m - 20 m = 10 m

In ∆CGD,

GD = 10 m, CG = 20 m ( radius )

CG² = GD² + CD²

20² - 10² = CD²

√300 = 10√3 m = CD

So, 2CD = BC

2 × 10√3 m = 20√3 m = BC

So length of string is 20√3 m.