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# Constructions

10th Class - CBSE - Mathematics - 239 Questions - 0 Concepts

#### Important Questions

Q1 Subjective Hard
If the sides of a parallelogram touch a circle. Prove that the parallelogram is a rhombus.

1 Verified Answer | Published on 07th 09, 2020

Q2 Subjective Hard
Construct a $\triangle ABC$ in which $AB =5\ cm$. $\angle B = 60^{\circ}$ altitude $CD = 3\ cm$. Construct a $\triangle AQR$ similar to $\triangle ABC$ such that side of $\triangle AQR$ is $1.5$ times that of the corresponding sides of $\triangle ACB$.

1 Verified Answer | Published on 07th 09, 2020

Q3 Subjective Hard
Draw a circle of radius 6 cm and construct tangents to it from an external point 10 cm away from the centre. Measure and verify the length of the tangents.

1 Verified Answer | Published on 07th 09, 2020

Q4 Subjective Hard
Construct a pair of tangents to a cricle of radius 3.5 cm from a point 3.5 cm away from the circle.

1 Verified Answer | Published on 07th 09, 2020

Q5 Subjective Hard
A pair of perpendicular tangents are drawn to a circle from an external point. Prove that length of each tangent is equal to the radius of the circle.

1 Verified Answer | Published on 07th 09, 2020

Q6 Subjective Hard
In the figure, if AB = AC prove that BQ = QC.

1 Verified Answer | Published on 07th 09, 2020

Q7 Subjective Hard
Draw a right triangle which the sides (other than hypotenuse) are of lengths $4\ cm$ and $3\ cm$. Then construct another triangle whose sides are $\cfrac{5}{3}$ times the corresponding sides of the given triangle.

1 Verified Answer | Published on 07th 09, 2020

Q8 Subjective Hard
Draw a $\triangle ABC$ with side $BC=7\ cm$, $\angle B={45}^{\circ}, \angle A={105}^{\circ}$. Then, construct a triangle whose sides are $\cfrac{4}{3}$ times the corresponding sides of $\triangle ABC$.

1 Verified Answer | Published on 07th 09, 2020

Q9 Subjective Hard
In the figure PQ, PR and BC are the tangents to the circle. BC touches the circle at X. If PQ = 7 cm, find the perimeter of $\triangle PBC$.

1 Verified Answer | Published on 07th 09, 2020

Q10 Subjective Hard
Construct tangents to a circle of radius $4\ cm$ at $Q$ and $R$, from a point $P$ on the concentric circle of radius $6\ cm$.