Constructions — Practice Quiz
ICSE · Class 10 · Mathematics
Try a 4-question quiz on Constructions for ICSE Class 10 Mathematics: tap an answer to check it and see why. 38 questions in the full chapter test.
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How many tangents can be drawn to a circle from an external point?
In the construction of tangents from external point P to a circle with center O, what is the first step?
What is the center of the auxiliary circle in tangent construction from external point P to circle with center O?
The radius of the auxiliary circle in tangent construction equals:
Sample Questions
Which of the following tools are required for constructing tangents to a circle from an external point?
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Compass, Ruler
The construction of tangents from an external point requires joining points with straight lines (using a ruler) and drawing circles/arcs of specific radii, such as the circle on OP as diameter and marking equal radii (using a compass). A protractor or set square is not needed since no angles are measured directly and no perpendicular lines from a set square are used in this method. Hence only the compass and ruler are the correct tools.
Which circles are involved in constructing tangents from an external point?
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Given circle with center O, Auxiliary circle with center M
Two circles are involved: the original given circle with center O, and the auxiliary circle with center at midpoint M of PO. These two circles intersect at points which help locate the tangent points.
How many tangents can be drawn to a circle from a point lying on the circle?
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1
From a point on the circle, exactly one tangent can be drawn. This tangent is perpendicular to the radius at that point.
The auxiliary circle intersects the given circle at how many points?
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2
The auxiliary circle intersects the given circle at exactly 2 points. These intersection points are the points of tangency for the two tangents from the external point.
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