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AB is a line segment of length 2a, with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is
  • a)
    2a/3
  • b)
    a/2
  • c)
    a/3
  • d)
    a/4
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
AB is a line segment of length 2a, with M as mid-point. Semicircles a...
Given:
AB is a line segment of length 2a.
Concept:
Pythagoras theorem: In an right - angled triangle
Hypotenuse2 = Base2 + Perpendicular2
Fomula used:
(a - b)2 = a2 - 2ab + b2
(a + b)2 = a2 + 2ab + b2
Calculation:
We know that, two circles touch each other externally if
Distance between their centres = Sum of their radii
⇒ OL = r + a/2 -----(1)
⇒ OM = CM - OC
⇒ OM = a - r -----(2)
⇒ LM = a/2 -----(3)
In △OML, using Pythagoras theorem
⇒ (OL)2 = (OM)2 + (LM)2
Using the formula disucssed above
∴ The value or r is a/3.
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Community Answer
AB is a line segment of length 2a, with M as mid-point. Semicircles a...
Given:
AB is a line segment of length 2a.
Concept:
Pythagoras theorem: In an right - angled triangle
Hypotenuse2 = Base2 + Perpendicular2
Fomula used:
(a - b)2 = a2 - 2ab + b2
(a + b)2 = a2 + 2ab + b2
Calculation:
We know that, two circles touch each other externally if
Distance between their centres = Sum of their radii
⇒ OL = r + a/2 -----(1)
⇒ OM = CM - OC
⇒ OM = a - r -----(2)
⇒ LM = a/2 -----(3)
In △OML, using Pythagoras theorem
⇒ (OL)2 = (OM)2 + (LM)2
Using the formula disucssed above
∴ The value or r is a/3.
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AB is a line segment of length 2a, with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r isa)2a/3b)a/2c)a/3d)a/4Correct answer is option 'C'. Can you explain this answer?
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Solutions for AB is a line segment of length 2a, with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r isa)2a/3b)a/2c)a/3d)a/4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL. Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free.
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