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

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