Give also the justification of the construction:
Draw a circle of radius $6 \, cm$. From a point $10 \, cm$ away from its centre,construct the pair of tangents to the circle and measure their lengths.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) pair of tangents to the given circle can be constructed as follows:
$1.$ Taking any point $O$ of the given plane as centre,draw a circle of $6 \, cm$ radius. Locate a point $P$,$10 \, cm$ away from $O$.
Join $OP$.
$2.$ Bisect $OP$. Let $M$ be the mid-point of $PO$.
$3.$ Taking $M$ as centre and $MO$ as radius,draw a circle.
$4.$ Let this circle intersect the previous circle at points $Q$ and $R$.
$5.$ Join $PQ$ and $PR$. $PQ$ and $PR$ are the required tangents.
The lengths of tangents $PQ$ and $PR$ are $8 \, cm$ each.
Justification:
The construction can be justified by proving that $PQ$ and $PR$ are the tangents to the circle (whose centre is $O$ and radius is $6 \, cm$). For this,join $OQ$ and $OR$.
$\angle PQO$ is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.
$\therefore \angle PQO = 90^{\circ}$
$\Rightarrow OQ \perp PQ$
Since $OQ$ is the radius of the circle,$PQ$ has to be a tangent to the circle. Similarly,$PR$ is a tangent to the circle.

Explore More

Similar Questions

Construct a triangle similar to a given triangle $ABC$ with its sides equal to $\frac{3}{4}$ of the corresponding sides of the triangle $ABC$ (i.e.,of scale factor $\frac{3}{4}$).

Construct a triangle similar to a given triangle $ABC$ with its sides equal to $\frac{5}{3}$ of the corresponding sides of the triangle $ABC$ (i.e.,of scale factor $\frac{5}{3}$).

Let $ABC$ be a right triangle in which $AB = 6 \, cm$,$BC = 8 \, cm$ and $\angle B = 90^{\circ}$. $BD$ is the perpendicular from $B$ on $AC$. The circle through $B, C, D$ is drawn. Construct the tangents from $A$ to this circle and provide the justification for the construction.

Difficult
View Solution

Draw a line segment of length $7.6 \, cm$ and divide it in the ratio $5: 8$. Measure the two parts and give the justification of the construction.

Draw a pair of tangents to a circle of radius $5\, cm$ which are inclined to each other at an angle of $60^{\circ}$. Also,provide the justification for the construction.

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo