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# Little Johnny wants to eat a candy (circular in shape) using chopstick

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Math Expert
Joined: 02 Sep 2009
Posts: 65014
Little Johnny wants to eat a candy (circular in shape) using chopstick  [#permalink]

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02 Jun 2020, 04:19
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Difficulty:

25% (medium)

Question Stats:

76% (01:23) correct 24% (02:10) wrong based on 17 sessions

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Little Johnny wants to eat a candy (circular in shape) using chopsticks! For this he makes sure that one end of either chopstick is touching the other (held in his hand) and the other end is used to hold the candy, as shown in the figure below. If his mom wants him to maintain a distance of at least 10 cm between his hands and his mouth while eating, what is the minimum length (in cm) of chopsticks required by him to eat the candy using chopsticks? (Assume that both the chopsticks are of equal length and that the radius of the candy is 6 cm.)

A. 8
B. 9
C. 10
D. 11
E. 12

Attachment:

1.png [ 18.79 KiB | Viewed 307 times ]

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Re: Little Johnny wants to eat a candy (circular in shape) using chopstick  [#permalink]

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02 Jun 2020, 04:51
The tangent subtends an angle of 90 degrees on the radius of the circle.
The next step is to use the pythagorus theorem.

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Re: Little Johnny wants to eat a candy (circular in shape) using chopstick  [#permalink]

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02 Jun 2020, 05:53
Bunuel wrote:

Little Johnny wants to eat a candy (circular in shape) using chopsticks! For this he makes sure that one end of either chopstick is touching the other (held in his hand) and the other end is used to hold the candy, as shown in the figure below. If his mom wants him to maintain a distance of at least 10 cm between his hands and his mouth while eating, what is the minimum length (in cm) of chopsticks required by him to eat the candy using chopsticks? (Assume that both the chopsticks are of equal length and that the radius of the candy is 6 cm.)

A. 8
B. 9
C. 10
D. 11
E. 12
Attachment:
1.png

Solution

• We need to find the length of the chopstick i.e. PT.
• To have minimum length of the PT, it should just be exactly equal to the length of the tangent to the circle.
• As PT is tangent to the circle, triangle OTP is a right-angled triangle, right angled at T.
o Thus, $$PT = \sqrt{10^2 – 6^2} = 8$$
Thus, the correct answer is Option A.
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Re: Little Johnny wants to eat a candy (circular in shape) using chopstick  [#permalink]

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02 Jun 2020, 07:45
IMO A

The angle between a tangent and a radius is 90°

So triangle POT is right angle triangle.

Using pythagoras theorem, OP^2 = OT^2 + PT^2
100 = 36 + PT^2

PT = 8
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Re: Little Johnny wants to eat a candy (circular in shape) using chopstick  [#permalink]

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02 Jun 2020, 08:41
Bunuel wrote:

Little Johnny wants to eat a candy (circular in shape) using chopsticks! For this he makes sure that one end of either chopstick is touching the other (held in his hand) and the other end is used to hold the candy, as shown in the figure below. If his mom wants him to maintain a distance of at least 10 cm between his hands and his mouth while eating, what is the minimum length (in cm) of chopsticks required by him to eat the candy using chopsticks? (Assume that both the chopsticks are of equal length and that the radius of the candy is 6 cm.)

A. 8
B. 9
C. 10
D. 11
E. 12

Attachment:
1.png

Use Pythagorean Triple set concept, (3,4,5)

So, Length for the chopstick will be (6,8,10) Multiply 2 * (3,4,5)

Hence, Answer must be (A) 8
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Re: Little Johnny wants to eat a candy (circular in shape) using chopstick   [#permalink] 02 Jun 2020, 08:41