(B) To construct a triangle similar to a given $\triangle ABC$ with a scale factor of $\frac{3}{7}$,we follow these steps:$1$. Draw a ray $BX$ making

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(B) To construct a triangle similar to a given $\triangle ABC$ with a scale factor of $\frac{3}{7}$,we follow these steps:$1$. Draw a ray $BX$ making an acute angle with $BC$.$2$. Locate $7$ points $(B_{1}, B_{2}, B_{3}, B_{4}, B_{5}, B_{6}, B_{7})$ on $BX$ at equal distances because the denominator of the fraction $\frac{3}{7}$ is $7$.$3$. The next step is to join the last point,$B_{7}$,to $C$ to establish the base line for the construction.

Class 10 Mathematics Constructions Mix Examples - Constructions

Medium

To construct a triangle similar to a given $\triangle ABC$ with its sides $\frac{3}{7}$ of the corresponding sides of $\triangle ABC$,first draw a ray $BX$ such that $\angle CBX$ is an acute angle and $X$ lies on the opposite side of $A$ with respect to $BC$. Then locate points $B_{1}, B_{2}, B_{3}, \dots$ on $BX$ at equal distances and the next step is to join

A
$B_{10}$ to $C$
B
$B_{7}$ to $C$
C
$B_{13}$ to $C$
D
$B_{4}$ to $C$

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Class 10

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Mix Examples - Constructions

Draw $\Delta PQR$ with $QR = 7 \, cm$,$m\angle Q = 45^{\circ}$ and $m\angle R = 60^{\circ}$. Then construct $\Delta QAB$ similar to $\Delta PQR$ whose sides have lengths $\frac{4}{3}$ times the lengths of corresponding sides of $\Delta PQR$. Write the steps of construction.

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Two line segments $AB$ and $AC$ include an angle of $60^{\circ}$ where $AB = 5 \, cm$ and $AC = 7 \, cm$. Locate points $P$ and $Q$ on $AB$ and $AC$,respectively,such that $AP = \frac{3}{4} AB$ and $AQ = \frac{1}{4} AC$. Join $P$ and $Q$ and measure the length $PQ$.

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Draw two concentric circles of radii $3\, cm$ and $5\, cm$. Taking a point on the outer circle,construct a pair of tangents to the other circle. Measure the length of a tangent and verify it by actual calculation.

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To divide a line segment $AB$ in the ratio $5: 6,$ draw a ray $AX$ such that $\angle BAX$ is an acute angle,then draw a ray $BY$ parallel to $AX$ and the points $A_{1}, A_{2}, A_{3}, \ldots$ and $B_{1}, B_{2}, B_{3}, \ldots$ are located at equal distances on ray $AX$ and $BY,$ respectively. Then the points joined are

Difficult

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$A$ circle $\odot(P, 4)$ is given. Draw a pair of tangents such that the measure of the angle between the tangents at their point of intersection $A$ is $60^\circ$.

Medium

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Draw $\Delta PQR$ with $QR = 7 \, cm$,$m\angle Q = 45^{\circ}$ and $m\angle R = 60^{\circ}$. Then construct $\Delta QAB$ similar to $\Delta PQR$ whose sides have lengths $\frac{4}{3}$ times the lengths of corresponding sides of $\Delta PQR$. Write the steps of construction.

Two line segments $AB$ and $AC$ include an angle of $60^{\circ}$ where $AB = 5 \, cm$ and $AC = 7 \, cm$. Locate points $P$ and $Q$ on $AB$ and $AC$,respectively,such that $AP = \frac{3}{4} AB$ and $AQ = \frac{1}{4} AC$. Join $P$ and $Q$ and measure the length $PQ$.

Draw two concentric circles of radii $3\, cm$ and $5\, cm$. Taking a point on the outer circle,construct a pair of tangents to the other circle. Measure the length of a tangent and verify it by actual calculation.

$A$ circle $\odot(P, 4)$ is given. Draw a pair of tangents such that the measure of the angle between the tangents at their point of intersection $A$ is $60^\circ$.

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