Question

3 girls A,B,C playing a game by standing on a circle of radius 20 m draw in a park. A throw a ball to B and B to C and then throw a ball to B if the distance between A and B,B and C each 24 m what is the distance between AC​

Answer 1

Answer:

★Question★

• 3 girls A,B,C playing a game by standing on a circle of radius 20 m in a park. A throw a ball to B and B to C and then C throw a ball to A, if the distance between A and B, B and C each 24 m what is the distance between A and C

Given :-

• Radius of circular park = 20 m
• Distance between A and B = 24 m
• Distance between B and C = 24 m

To Find :-

• Distance between A and C.

Construction:-

Draw angle bisector of /_ABC .

So it passes through centre 0 and perpendicular bisector of AC. Let it meet AC at D. Join OA.

⟹ AD = DC = 1/2 AC

Solution :-

Let OD = x and AD = y

As OB = 20

⟹ BD = 20 - x

In right ∆AOD

★By pythagoras theorem,

⇛AO² = OD² + AD²

⇛400 = x² + y².....(1)

In right ∆ABD

★By pythagoras theorem,

⇛AB² = AD² + BD²

⇛24² = y² + (20 - x)²

⇛576 = y² + 400 + x² - 40x

⇛576 - 400 = 400 - 40x (using (1))

⇛176 = 400 - 40x

⇛ 40x = 224

⇛x = 28/5 m.......(2)

Put (2) in (1) we get

⇛ 400 = (28/5)² + y²

⇛ 400 - 784/25 = y²

⇛ y² = (10000 - 784)/25

⇛ y² = 9216/25

⇛ y = 96/5 m

So Distance between A and C = 2y = 2 × 96/5 = 192/5 m