Question

Three Students Priyanka. Sania and David are
Protesting against killing innocent animals for
commercial purposes in a circular park of radius 20 m.
They are standing at equal distance on its boundary
by holding banners in their hands.
(i) Find the distance between cach of them?
(ii) Which mathematical concept is used in it?​

Answer 1

Step-by-step explanation:

Three Students Priyanka. Sania and David are  Protesting against killing innocent animals for  commercial purposes in a circular park of radius 20 m.  They are standing at equal distance on its boundary  by holding banners in their hands.

(i) Find the distance between each of them?

(ii) Which mathematical concept is used in it?​

• Assume P,S and D be the positions of Priyanka, Sania and David on the boundary of circular park with centre O.
• Draw PQ  perpendicular to SD.
• Since the circle coincides with the centroid of equilateral triangle ABC
• Therefore radius of circumscribed circle = 2/3 PQ.
•    20 = 2/3 PQ
• SD = 20 x 3/2  
• So SD = 30 m
• Now let PS = SD = DP = x m
• SQ = QD = 1/2 SD  
•                 = x/2
• In right triangle SQP, angle Q = 90 degree.
• Therefore by Pythagoras theorem we get
• PS^2 = SQ^2 + PQ^2  
• So x^2 = (x/2)^2 + (30)^2
• So x^2 – x^2/4 = 900
• Or x^2 = 900 x 4/3
• Or x^2 = 1200
• Or x = √1200
•            = 20 √3

So distance between each of them is 20√3 m

Properties of circle, equilateral triangle and Pythagoras theorem are used.

Answer 2

answer :

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