Question

Three scouts Razat, Rohit, and Ramit in the cultural show with three stringed balloons with a message ‘stop child labour’, keeping themselves on the boundary of circle of radius 25cm. Find the distance between Razat and Ramit when distance between Razat and Rohit and Rohit and Ramit is 30cm.
A. 24
B. 48
C. 36
D. 12​

Answer 1

Answer:

48 cm

Step-by-step explanation:

Answer 2

Given:

Razat, Rohit, and Ramit are standing on the boundary of a circle of radius 25cm.

The distance between Razat and Rohit and Rohit and Ramit is 30cm.

To Find:

The distance between Razat and Ramit

Solution:

Let the positions of Razat, Rohit, and Ramit on the circle be P, Q, and R as shown in the diagram below.

Let O be the center of the circle.

According to the question,

PQ = QR = 30cm

Also, OQ is the perpendicular bisector of PR

Let OQ bisect PR at S

Applying Pythagoras theorem in ΔPSQ

PS² = PQ² - SQ²

PS² = 900 - SQ²      - (1)

Again applying Pythagoras theorem in ΔOSP

PS² = OP² - OS²

= 625 - (OQ - SQ)²       - (2)

Equating equations 1 and 2 we get,

900 - SQ²  = 625 - (25 - SQ)²

900 - SQ² = 625 - 625 - SQ² + 50 SQ

or 50 SQ = 900

or SQ = 18 cm

Substituting the value of SQ in equation 1,

PS² = 900 - 324

= 576

Taking square roots on both sides,

PS = 24

The distance between Razat and Ramit is PR = 2 X PS = 2 X 24

= 48cm

Hence, the distance between Razat and Ramit is (b) 48cm.