Question

in a circular park there are three girls reshma salma and mandeep they play a game of passing a ball reshma throws ball to mandeep and mandeep to salma and salma to mandeep distance between reshma salma is 6 m and radius of park is 5 m find the distance between reshma to salma

Answer 1

Answer:

Distance between Reshma and Mandeep is 9.6 m.

Step-by-step explanation:

Given :-

Distance between Reshma and salma and between salma and mandeep is 6 m.

Radius of circle is 5 m.

To find :-

Distance between Reshma and mandeep.

Solution :-

Let, Point where Reshma, salma and mandeep are standing be R, S and M respectively.

And Centre of circle be A.

Construction :- Draw perpendicular AB on RS.

The perpendicular from the center of a circle to a chord bisects the chord.

RS is cord. Then RB and BS are equal.

$\leadsto$ RS = RB + BS = 6 m

$\leadsto$ RB = BS = 3 m.

In ∆RBA,

By Pythagoras theorem :

Perpendicular² = Hypotenuse² - Base²

Perpendicular = AB

Base = RS = 3 m

Hypotenuse = AR = 5 m

$\longrightarrow$ (AB)² = (AR)² - (RS)²

$\longrightarrow$ AB² = (5)² - (3)²

$\longrightarrow$ AB² = 25 - 9

$\longrightarrow$ AB² = 16

$\longrightarrow$ AB = √16

$\longrightarrow$ AB = 4

Measure of AB is 4 m.

In ∆SAR,

We know,

Area of triangle = ½ × base × height

Base = RS

Height = AB

$\longrightarrow$ ½ × 4 × 6

$\longrightarrow$ 2 × 6

$\longrightarrow$ 12

Area of ∆SAR is 12 m².

If we see triangle taking base AS and height be RO than area will be same.

So,

$\longrightarrow$ ½ × RO × 5 = 12

$\longrightarrow$ RO × 5 = 12 × 2

$\longrightarrow$ RO × 5 = 24

$\longrightarrow$ RO = 24/5

$\longrightarrow$ RO = 4.8

Measure of RO is 4.8 m.

In Quadrilateral RSMA

RS = MS = 6 m [Given]

RS = AM = 5 m [Radius of circle]

We know,

Kite is only quadrilateral whose pair of adjacent sides are equal.

Thus,

RSMA is a kite.

And,

Diagonals of kite bisect each other at right angle

So, Diagonals are SA and RM,

Then, RO = MO

RO is 4.8 m.

Than,

MO = 4.8 m.

Now,

Distance between Reshma and Mandeep = RO + MO

= 4.8 + 4.8

= 9.6

Therefore,

Distance between Reshma and Mandeep is 9.6 m.