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# Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

**Solution:**

Perpendicular from center to either of the chord bisects the chord. Using this fact and the Pythagoras theorem, we can find the distance between Reshma and Mandip.

Let O be the center of the circle, and R, M and S denote Reshma, Mandip, and Salma respectively.

Draw a perpendicular OA to RS from O. Then RA = AS = 3 m.

Using the Pythagoras theorem, we get OA = 4 m.

We can see that quadrilateral ORSM takes the shape of a kite. (Because OR = OM and RS = SM).

We know that the diagonals of a kite are perpendicular, and the main diagonal bisects the other diagonal.

∠RNS will be 90° and RN = NM

Area of ∆ORS = 1/2 × RS × OA

= 1/2 × 6 × 4

= 12 …(1)

Also

Area of ∆ORS = 1/2 × OS × RN

= 1/2 × 5 × RN …(2)

From equation (1) and (2)

(1/2) × 5 × RN = 12

RN = 24/5 = 4.8m

RM = 2 × RN = 2 × 4.8 = 9.6 m

Distance between Reshma and Salma is 9.6 m.

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 10

**Video Solution:**

## Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?

Maths NCERT Solutions Class 9 Chapter 10 Exercise 10.4 Question 5

**Summary:**

If three girls Reshma, Salma, and Mandip, are playing a game by standing on a circle of radius 5m drawn in a park, Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma, and the distance between Reshma and Salma and between Salma and Mandip is 6m each, then the distance between Reshma and Mandip is 9.6m.

**☛ Related Questions:**

- Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centers is 4 cm. Find the length of the common chord.
- If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
- If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the center makes equal angles with the chords.
- If a line intersects two concentric circles (circles with the same center) with center O at A, B, C and D, prove that AB = CD.

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