Class 10 Maths MCQ Question of Constructions are given here with answers and detailed explanations. All these MCQ Questions are available online as per the CBSE syllabus and NCERT guidelines. Solving these objective questions will help students to score better marks in the board exam.

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**A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?**

(a) 1

(b) 3

(c) Infinite

(d) 2**In division of a line segment AB, any ray AX making angle with AB is**

(a) right angle

(b) obtuse angle

(c) any arbitrary angle

(d) acute angle

**To divide a line segment AB in the ratio 3:4, first, a ray AX is drawn so that****∠****BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is:**

(a) 5

(b) 7

(c) 9

(d) 11

**To divide a line segment AB of length 7.6 cm in the ratio 5 : 8, a ray AX is drawn first such that****∠****BAX forms an acute angle and then points A**_{1}, A_{2}, A_{3}, ….are located at equal distances on the ray AX and the point B is joined to:

(a) A_{5}

(b) A_{6}

(c) A_{10}

(d) A_{13}

**To construct a triangle similar to a given ΔPQR with its sides 5/8 of the similar sides of ΔPQR, draw a ray QX such that****∠****QRX is an acute angle and X lies on the opposite side of P with respect to QR. Then locate points Q**_{1}, Q_{2}, Q_{3}, … on QX at equal distances, and the next step is to join:

(a) Q_{10} to C

(b) Q_{3} to C

(c) Q_{8} to C

(d) Q_{4} to C

**To divide a line segment AB in the ratio 5:7, first a ray AX is drawn so that****∠****BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is:**

(A) 8

(B) 10

(C) 11

(D) 12

**To divide a line segment AB in the ratio 4:7, a ray AX is drawn first such that****∠****BAX is an acute angle and then points A**_{1}, A_{2}, A_{3}, ….are located at equal distances on the ray AX and the point B is joined to

(A) A_{12}

(B) A_{11}

(C) A_{10 }

(D) A_{9}

**To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°. It is required to draw tangents at the end points of those two radii of the circle, the angle between which is**

(a) 105°

(b) 70°

(c) 140°

(d) 145°

**To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be**

(a) 135°

(b) 90°

(c) 60°

(d) 120°

**To construct a triangle similar to a given ΔPQR with its sides, 9/5 of the corresponding sides of ΔPQR draw a ray QX such that****∠****QRX is an acute angle and X is on the opposite side of P with respect to QR. The minimum number of points to be located at equal distances on ray QX is:**

(a) 5

(b) 9

(c) 10

(d) 14

**To divide a line segment PQ in the ratio m : n, where m and n are two positive integers, draw a ray PX so that****∠****PQX is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is:**

(a) m + n

(b) m – n

(c) m + n – 1

(d) Greater of m and n

**To draw a pair of tangents to a circle which are inclined to each other at an angle of 45°, it is required to draw tangents at the endpoints of those two radii of the circle, the angle between which is:**

(a) 135°

(b) 155°

(c) 160°

(d) 120°

**A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of ___________ from the centre.**

(a) 3.5 cm

(b) 2.5 cm

(c) 5 cm

(d) 2 cm

**To construct a triangle similar to a given ΔABC with its sides 8/5 of the corresponding sides of ΔABC draw a ray BX such that****∠****CBX is an acute angle and X is on the opposite side of A with respect to BC. The minimum number of points to be located at equal distances on ray BX is:**

(A) 5

(B) 8

(C) 13

(D) 3

**Which theorem criterion we are using in giving the just the justification of the division of a line segment by usual method ?**

(a) SSS criterion

(b) Area theorem

(c) BPT

(d) Pythagoras theorem

**A point P is at a distance of 8 cm from the centre of a circle of radius 5 cm. How many tangents can be drawn from point P to the circle?**

(a) 0

(b) 1

(c) 2

(d) Infinite

**A line segment drawn perpendicular from the vertex of a triangle to the opposite side is called the**

(a) Bisector

(b) Median

(c) Perpendicular

(d) Altitude

**If the scale factor is 3/5, then the new triangle constructed is _____ the given triangle.**

(a) smaller the

(b) greater than

(c) overlaps

(d) congruent to

**By geometrical construction, which one of the following ratios is not possible to divide a line segment?**

(a) 1 : 10

(b) √9 : √4

(c) 10 : 1

(d) 4 + √3 : 4 – √3

**In constructions, the scale factor is used to construct ______ triangles.**

(a) right

(b) equilateral

(c) similar

(d) congruent

**Answer:**

**Answer:**(a) 2**Answer:**(d) acute angle**Answer:**(b) 7

**Explanation: **We know that to divide a line segment in the ratio m: n, first draw a ray AX which makes an acute angle BAX, then we are required to mark m + n points at equal distances from each other.

Here, m = 3, n = 4

So, the minimum number of these points = m + n = 3 + 4 = 7

**Answer:**(d) A_{13}

**Explanation: **The minimum points located in the ray AX is 5 + 8 = 13. Hence, point B will join point A_{13}.

**Answer:**(c) Q_{8}to C

**Explanation:** Here we locate points Q_{1}, Q_{2}, Q_{3}, Q_{4}, Q_{5}, Q_{6}, Q_{7} and Q_{8} on QX at equal distances and in the next step join the last point Q_{8} to R.

**Answer:**(D) 12

**Explanation: **We know that to divide a line segment in the ratio m : n, first draw a ray AX which makes an acute angle BAX , then marked m+n points at equal distances from each other.

Here m = 5, n = 7

So minimum number of these point = m + n = 5 + 7 = 12

**Answer:**(B) A_{11}

**Explanation: **Here minimum 4+7=11 points are located at equal distances on the ray AX and then B is joined to last point, i.e., A_{11}.

**Answer:**(d) 145°**Answer**:(d) 120°**Answer:**(b) 9

**Explanation: **To draw a triangle similar to a given triangle with its sides m/n of the similar sides of a given triangle, the minimum number of points to be located at an equal distance is equal to m or n, whichever is greater.

Here, m/n = 9/5

9 > 5, therefore the minimum number of points to be located is 9.