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# To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A_{1} , A_{2} , A_{3} , ... and B_{1} , B_{2} , B_{3} , ... are located at equal distances on ray AX and BY, respectively. Then the points joined are

a. A_{5 }and B_{6}

b. A_{6 }and B_{5}

c. A_{4 }and B_{5}

d. A_{5 }and B_{4}

**Solution:**

It is given that

__Line segment__ AB is divided in the ratio 5: 6

A: B = 5: 6

Steps of Construction:

1. Construct a ray AX and an __acute angle__ BAX.

2. Construct a ray BY || AX and ∠ABY = ∠BAX.

3. Let us locate the points A_{1}, A_{2}, A_{3}, A_{4} and A_{5} on AX and B_{1}, B_{2}, B_{3}, B_{4}, B_{5} and B_{6} as A: B = 5: 6

4. Now join A_{5}B_{6}.

5. Here A_{5} B_{6} intersects AB at the point C.

AC: BC = 5: 6

Therefore, the points joined are A_{5} and B_{6}.

**✦ Try This: **To divide a line segment AB in the ratio 3: 2, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A_{1}, A_{2}, A_{3}, ... and B_{1}, B_{2}, B_{3}, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 11

**NCERT Exemplar Class 10 Maths Exercise 10.1 Problem 3**

## To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A_{1} , A_{2} , A_{3} , ... and B_{1} , B_{2} , B_{3} , ... are located at equal distances on ray AX and BY, respectively. Then the points joined are a. A_{5} and B_{6}, b. A_{6} and B_{5}, c. A_{4} and B_{5}, d. A_{5} and B_{4}

**Summary:**

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A_{1} , A_{2} , A_{3} , ... and B_{1} , B_{2} , B_{3} , ... are located at equal distances on ray AX and BY, respectively. Then the points joined are A_{5} and B_{6}

**☛ Related Questions:**

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