Class 10 Constructions — practice questions with answers
Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. What is the first step in dividing a line segment into a ratio of 4:3?
ADraw a ray from one endpoint making an acute angle with the segment
BDraw a circle with the segment as diameter
CMeasure the segment with a ruler
DDraw an arc from the midpoint
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Answer: A) Draw a ray from one endpoint making an acute angle with the segment
To divide a segment into a ratio, start by drawing a ray from one endpoint making an acute angle with the segment, then mark equal arcs on it.
2. To construct a triangle similar to a given triangle with scale factor 43 (smaller), how many equal arcs are marked on the auxiliary ray?
A3
B5
C4
D8
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Answer: C) 4
For scale factor nm the number of equal divisions on the ray is the greater of m and n. For 43, that is 4.
3. Which statement is CORRECT about a secant of a circle, as opposed to a tangent?
AA secant intersects the circle at two points while a tangent touches at one point
BA secant touches the circle at exactly one point
CA secant never meets the circle
DA secant is always perpendicular to the radius
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Answer: A) A secant intersects the circle at two points while a tangent touches at one point
A secant cuts the circle at two distinct points; a tangent meets it at exactly one point of contact.
4. Each side of a new triangle must be 53 of the corresponding side of triangle ABC, and five points have already been marked on the ray BX. Which point is joined to C before the parallel line is drawn?
AB5
BB3
CB15
DB2
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Answer: A) B5
When the scale factor is less than 1 the LAST point is joined to C, so B5C is drawn; the parallel through B3 then cuts BC itself at C' with BC' = 53BC. Joining B3 is the rule for an enlarging factor such as 35, and it is the pairing of these two cases that is most often mixed up.
5. When a tangent is constructed at a point A of a circle, why is the drawn line made perpendicular to the radius OA?
ABecause a perpendicular is the shortest line that can be drawn from O to any line
BBecause every chord of the circle is perpendicular to a radius
CBecause the perpendicular at A passes through the centre of the circle
DBecause the tangent at any point of a circle is perpendicular to the radius through that point
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Answer: D) Because the tangent at any point of a circle is perpendicular to the radius through that point
The step simply applies the tangent-radius theorem: at the point of contact the tangent and the radius meet at 90 degrees. It is true that OA then becomes the shortest distance from O to the tangent, but that is a consequence of the theorem rather than the reason for the step, and a tangent never passes through the centre.