Constructions

Q1.For what value of n is it impossible to construct a tangent from an external point to a circle of radius n when the external point is at distance n from the center?

• AWhen n = 0
• BWhen external point is ON the circle
• CWhen the point is inside the circle
• DWhen n > 0

Q2.To construct a triangle with sides in ratio 5:3 to a given triangle ABC, the scale factor is:

• A5/3
• B3/5
• C5+3 = 8
• D5−3 = 2

Q3.To draw a tangent at point P on a circle with center O (when center is known), we draw OP and then construct a perpendicular to OP at P. The perpendicular is drawn using:

• AA ruler and set square
• BCompass and ruler to construct a 90° angle
• CAngle bisector of ∠OPB (for any point B)
• DBoth a and b are acceptable

Q4.How many tangents can be drawn from a point outside a circle?

• A0
• B1
• C2
• DInfinite

Q5.In the basic construction of a similar triangle (scale factor m/n, m > n), we mark m points on the ray. Why m points and not m+n?

• ABecause we're enlarging, not dividing
• BBecause n is not used in enlargement
• CWe mark n points from the vertex
• DIt depends on the specific construction