$AC$ and $BD$ are two perpendicular diameters of a circle with centre $O$. If $AC = 16 \ cm$, calculate the area and perimeter of the shaded part. (Take $\pi = 3.14).$
View full solution →Question types
constructions-circle question types
33 questions across 3 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.
33
Questions
3
Question groups
5
Question types
Sample Questions
constructions-circle questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The diagram represents the area swept by wiper of a car. With the dimension given in figure, calculate the shaded swept by the wiper.
$AC$ and $BD$ are two perpendicular diameter of a circle $ABCD.$ Given that the area of shaded portion is $308\ cm^2$ calculate:
(i) The length of $AC$ and
(ii) The circumference of circle
View full solution →(i) The length of $AC$ and
(ii) The circumference of circle
In the figure alongside, OAB is a quadrant of a circle. The radius $OA = 3.5 cm$ and $OD = 2 cm$. Calculate the area of the shaded $22$ portions.
View full solution →Four equal circles, each of radius $5 cm$, touch each other as shown in the figure. Find the area included between them. (Take $π= 3.14$)
View full solution →Use a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ ABC = 60°, and AB 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ ABC of Δ ABC.
Draw a circle at a radius of 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.
Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
Use ruler and compasses only for this question:
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC, and also equidistant from B and C. Measure and record the length of PB.
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC, and also equidistant from B and C. Measure and record the length of PB.
Draw a circle of radius 2.5 cm and circumscribe a regular hexagon about it.
Draw a circle at a radius of 3 cm. Take a point at 5.5 cm from the center at the circle. From point P, draw two tangents to the circle.
Construct a ΔABC with base BC = 3.5 cm, vertical angle ∠ BAC = 45°, and median through the vertex A is 3.5 cm. Write also the steps of construction.
Draw a circle of radius 3 cm and construct a tangent to it from an external point without using the center.
Using a ruler and compasses only:
(i) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ ABC = 120°.
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure ∠ BCP.
(i) Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ ABC = 120°.
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure ∠ BCP.
The center O of a circle of a radius 1.3 cm is at a distance of 3.8 cm from a given straight line AB. Draw a circle to touch the given straight line AB at a point P so that OP = 4.7 cm and to touch the given circle externally.
Generate a constructions-circle paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.