## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 45 of Multiple Choice Questions (MCQ)

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

45
##### In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60°. The length of chord AB is

In the given Figure,

As PA and PB are tangents from common external point P, we have

PA = PB

[ tangents drawn from an external point are equal]

PBA = PAB

[ Angles opposite to equal sides are equal]

Now,

In APB, By Angle sum Property of triangle

APB + PBA + PAB = 180°

60° + PAB + PAB = 180°

2 PAB = 120°

PAB = 60°

So, We have

PBA = PAB = APB = 60°

i.e. APB is an equilateral triangle

so, we have

PA = PB = AB = 5 cm [ As PA = 5 cm ]

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The text passage contains a mathematical question about the length of a chord in a circle, and it provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Book: RS Aggarwal - Mathematics

### Chapter: 12. Circles

#### Subject: Maths - Class 10th

##### Q. No. 45 of Multiple Choice Questions (MCQ)

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

45
##### In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and ∠APB = 60°. The length of chord AB is

In the given Figure,

As PA and PB are tangents from common external point P, we have

PA = PB

[ tangents drawn from an external point are equal]

PBA = PAB

[ Angles opposite to equal sides are equal]

Now,

In APB, By Angle sum Property of triangle

APB + PBA + PAB = 180°

60° + PAB + PAB = 180°

2 PAB = 120°

PAB = 60°

So, We have

PBA = PAB = APB = 60°

i.e. APB is an equilateral triangle

so, we have

PA = PB = AB = 5 cm [ As PA = 5 cm ]

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user
The text passage contains a mathematical question about the length of a chord in a circle, and it provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER