4GMAT Diagnostic Test Q11 - Problem Solving - Geometry circles and triangles
25
GMAT QUANTITATIVE REASONING GEOMETRY - CIRCLES PROBLEM SOLVING Diagnostic Test
Transcript of 4GMAT Diagnostic Test Q11 - Problem Solving - Geometry circles and triangles
GMAT QUANTITATIVE REASONING
GEOMETRY - CIRCLES
PROBLEM SOLVING
Diagnostic Test
Question
What is the length of the chord AB if/AOB = 90°? O is the centre of the circleand the radius of the circle is 6 cm.
A. 12 cm
B. 6 cm
C. 3 cm
D.6
2E. 6 2
What is the approach?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
01 What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
01 What kind of a triangle is AOB?
02 Is it any special triangle?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
01 What kind of a triangle is AOB?
02 Is it any special triangle?
03 If so apply any relevant property of the special triangle and find the answer.
Part 1
What kind of a triangle is AOB?
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
Two sides of the triangle are equal·
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
Two sides of the triangle are equal· Triangle AOB is isosceles
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
Two sides of the triangle are equal· Triangle AOB is isosceles
/AOB = 90°. So, AOB is a right
triangle
What kind of a triangle is AOB?
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
Two sides of the triangle are equal· Triangle AOB is isosceles
/AOB = 90°. So, AOB is a right
triangleTherefore, AOB is a right isosceles triangle
What kind of a triangle is AOB?
Ratio of the sides of a right isosceles triangle
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
Two sides of the triangle are equal· Triangle AOB is isosceles
/AOB = 90°. So, AOB is a right
triangleTherefore, AOB is a right isosceles triangle
What kind of a triangle is AOB?
Ratio of the sides of a right isosceles triangle
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· OA is radius of the circle · OB is also radius of the circle
Two sides of the triangle are equal· Triangle AOB is isosceles
/AOB = 90°. So, AOB is a right
triangleTherefore, AOB is a right isosceles triangle
Sides opposite 450 – 450 – 900 are in the ratio
1 : 1 : 2
Part 2
Compute the length of chord AB
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· Ratio of the sides of a right isosceles triangle 1 : 1 : 2
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· Ratio of the sides of a right isosceles triangle 1 : 1 : 2
· In this triangle, OA : OB : AB : : 1 : 1 : 2
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· Ratio of the sides of a right isosceles triangle 1 : 1 : 2
· In this triangle, OA : OB : AB :: 1 : 1 : 2
· OA and OB are radii and measure 6 cm
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· Ratio of the sides of a right isosceles triangle 1 : 1 : 2
· In this triangle, OA : OB : AB :: 1 : 1 : 2
· OA and OB are radii and each measure 6 cm
· Therefore, AB the side opposite 900 will measure 6 2 cm
Length of chord AB is 6 2 cm
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· Ratio of the sides of a right isosceles triangle 1 : 1 : 2
· In this triangle, OA : OB : AB :: 1 : 1 : 2
· OA and OB are radii and measure 6 cm
· Therefore, AB the side opposite 900 will measure 6 2 cm
Choice E
Length of chord AB is 6 2 cm
What is the length of the chord AB?/AOB = 90°. Radius is 6 cm. O is the centre of the circle.
· Ratio of the sides of a right isosceles triangle 1 : 1 : 2
· In this triangle, OA : OB : AB :: 1 : 1 : 2
· OA and OB are radii and measure 6 cm
· Therefore, AB the side opposite 900 will measure 6 2 cm
For GMAT Prep
Visit http://www.4gmat.com
GMAT Classes and GMAT Preparation
Send your comments / feedback to
4GMATWe offer classroom training in Chennai and Bangalore
Tutors include GMAT 98%ilers, US B School graduates and IIM graduates
Call us: +91 95000 48484
Mail us: [email protected]
