The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer?

EduRev

All Courses

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > The figure above shows a circle whose diamete...

Join the Discussion on the App

The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?

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

FREE This question is part of

Test: Coordinate Geometry- 2

Attempt Test

Attempt this Test

Verified Answer

The figure above shows a circle whose diameter AB lies on the x-axis a...

Given

Circle with diameter AB
- Length of the diameter = AB = 4 units
Right triangle ACB
- ∠CAB = 30
Hypotenuse AB = 4 units

To Find : y – coordinate of point C

Approach:

Since AB coincides with the x-axis, the y-coordinate of point C will be equal to the perpendicular distance of point C from AB

So, referring to the above figure, we can write: y – coordinate of point C = CP
So, in order to answer the question, we need to know the value of CP

Now, area of right triangle ACB = ½ * AB * CP
- We already know the measure of AB. So, if we find the area of the triangle, we’ll be able to find CP
We can write another expression for the area of right triangle ACB:
- Area of right triangle ACB = ½ * AC * BC
In right triangle ACB, we know the measure of side AB and angle CAB = 30 and angle ACB = 90^o
- Thus, angle ABC = 180^o – 30^o – 90^o = 60^o
- WE can conclude that triangle ABC is a 30-60-90 Triangle.
- So, using the side ratio property of 30-60-90 Triangle, we can easily find AC and BC, and hence the area of the triangle.

Working out:

Finding BC and AC
In right triangle ACB,

BC : AC : AB = 1 : √3 : 2
- BC : AB = 1 : 2
- Since AB = 4
- So, BC = 2 units
AC : AB = √3 : 2
- Since AB = 4
- So, AC = 2√3units

1. Finding the area of triangle ACB
Area of right triangle ACB = ½ AC * BC = ½ * 2√3 * 2 =
2√3 square units

2. Finding CP
½ * CP * AB = 2√3 square units
½ *CP * 4 = 2√3
CP = √3 units

3. Getting to the answer
Therefore, the y-coordinate of point C =CP = √3 units
Looking at the answer choices, we see that the correct answer is OPTION D

View all questions of this test

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

In the xy-coordinate plane, polygon APBCDA is formed by placing rectangle ABCD and triangle APB as shown above. If sides AB and AD are parallel to the x- and the y- axes respectively, what is the area of polygon APBCDA?(1) The coordinates of points A and C are (6, 8) and (12, 12) respectively(2) The coordinates of point P are (8, 10)

View answer

In the figure above, triangle ABC is inscribed in a circle whose centre O has the x- and y-coordinates as (0,0). If the x- and y- coordinates of point A are (-4,0) and ∠BAC = 30, what is the area, in square units, of triangle AOB?

View answer

The figure above shows a rectangle ABCD in the xy- coordinate plane. The sides AB and AD are parallel to the x- and the y- axis respectively. How many squares of side 1 unit that lie on or inside the rectangle ABCD can be drawn?(1) The length of side AB is 6 units(2) The coordinates of points A and C are (3,2) and (9, 5)

View answer

Regular hexagon ABCDEF is symmetrical about the x-axis and the y-axis in a rectangular coordinate plane, as shown above. If the coordinates of point D are (2,0), what is the area, in square units, of rectangle BCEF?

View answer

In a rectangular coordinate plane, AB is the diameter of a circle and point C lies on the circle. If the coordinates of points A and B are (-1,0) and (5,0), and the area of triangle ABC is 6√2 square units, which of the following can be the coordinates of point C?

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

Share with a Friend

Answer this doubt

Question Description
The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer?.

Solutions for The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The figure above shows a circle whose diameter AB lies on the x-axis as shown. Triangle ACB is a right-angled triangle whose side AC makes an angle of 30? with side AB. If the coordinates of points A and B are (0,0) and (4,0) respectively, what is the y-coordinate of point C?a)b)c)d)e)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam