The figure above shows a circle whose centre O has the x- and y- coordinates as (6,0). Points A(m,n) and B(8,2) are marked on the circle such that andang;AOB = 105. If the circle is symmetrical about the x-axis, what is the value of m?a)2b)andradic;6c)4d)6 - andradic;6e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?

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The figure above shows a circle whose centre O has the x- and y- coordinates as (6,0). Points A(m,n) and B(8,2) are marked on the circle such that ∠AOB = 105^∘. If the circle is symmetrical about the x-axis, what is the value of m?

a)
2
b)
√6
c)
4
d)
6 - √6
e)
Cannot be determined

Correct answer is option 'D'. Can you explain this answer?

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The figure above shows a circle whose centre O has the x- and y- coord...

Given:

Circle
- Center = O(6,0)
- Points on the circle: A(m,b) and B(8,2)
  - This means, OA = OB = radius of circle
- ∠AOB = 105∘

To find: m = ?

Approach:

Let’s drop a perpendicular from point A on the x-axis.

From this diagram, it’s clear that there are 2 ways to find the value of m:

Way 1 – In right triangle AFO, if we can know the measure of one angle (out of ∠AOF and ∠OAF) and one side (like the radius AO), we can use trigonometric ratios to find length OF, and hence the value of m (since OF = 6 – m)
Way 2 – In right triangle AFO, if we can know the measure of sides AO (radius of circle) and AF, we can use Pythagoras Theorem to find OF, and hence m.

2. We are given the coordinates of both points O and B. So, using these, we can find the radius OB = OA

3. Also, if we drop a perpendicular from point B on the x-axis, we’ll know the magnitude of all the sides of the resulting right triangle.

So, we can use trigonometric ratios to find ∠BOE.

So, we can find ∠AOF using the equation

(Thus, in this Approach, we’re using Way 1 to find m)

Working Out:

Radius OB = OA = 2√2

Looking at the answer choices, we see that the correct answer is Option D

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The figure above shows a circle whose centre O has the x- and y- coordinates as (6,0). Points A(m,n) and B(8,2) are marked on the circle such that ∠AOB = 105∘. If the circle is symmetrical about the x-axis, what is the value of m?a)2b)√6c)4d)6 - √6e)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?

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