# Chord AB subtends ∠AOB = 60° at centre. If OA = 5 cm then find the length of AB (in cm).

2
by pravin3103

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2014-12-28T11:23:28+05:30

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∠AOB = 60°
OA =radius = 5 cm
OB = 5 cm

Since OA=OB, it is a isosceles triangle.
∠ABO = ∠BAO

In the triangle,
∠AOB +∠ABO + ∠BAO = 180°
So ∠ABO + ∠BAO = 180-60 = 120
∠ABO = 120/2 = 60 and
∠BAO = 60

SO it is an equilateral triangle. So all sides are equal.
Hence AB = 5cm
2014-12-28T14:47:00+05:30
Let the triangle be AOB where ∠AOB = 60°
Then we have AO = BO = 5 cm
Since Δ AOB is a isosceles triangle.
∠ABO = ∠BAO = (180-60)/2 = 60  degree
Hence we have, ΔAOB is an equiangular triangle hence an equilateral triangle where all sides are equal ⇒ AO = BO = AB = 5 cm
Length of AB is 5 cm
The text passage contains a geometry problem and its solution, where the length of a chord AB is calculated given the angle subtended at the center and the radius of the circle.
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Given a text passage, determine:
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    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:
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# Chord AB subtends ∠AOB = 60° at centre. If OA = 5 cm then find the length of AB (in cm).

2
by pravin3103

## Answers

The Brainliest Answer!
2014-12-28T11:23:28+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
∠AOB = 60°
OA =radius = 5 cm
OB = 5 cm

Since OA=OB, it is a isosceles triangle.
∠ABO = ∠BAO

In the triangle,
∠AOB +∠ABO + ∠BAO = 180°
So ∠ABO + ∠BAO = 180-60 = 120
∠ABO = 120/2 = 60 and
∠BAO = 60

SO it is an equilateral triangle. So all sides are equal.
Hence AB = 5cm
2014-12-28T14:47:00+05:30
Let the triangle be AOB where ∠AOB = 60°
Then we have AO = BO = 5 cm
Since Δ AOB is a isosceles triangle.
∠ABO = ∠BAO = (180-60)/2 = 60  degree
Hence we have, ΔAOB is an equiangular triangle hence an equilateral triangle where all sides are equal ⇒ AO = BO = AB = 5 cm
Length of AB is 5 cm
user
The text passage contains a geometry problem and its solution, where the length of a chord AB is calculated given the angle subtended at the center and the radius of the circle.

TYPE: SINGLE_QUESTION_WITH_ANSWER