Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60 degree Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents

Q: Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is $60^{\circ}$. Also, justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.

Answers (1)

Solution

Steps of construction:
1. Construct a circle with $O$ as a centre and a 4 cm radius
2. Construct any diameter $A O B$
3. Construct an angle $\angle A O P=600$ where $O P$ is the radius which intersect the circle at the point $P$
4. Construct $P Q$ perpendicular to $O P$ and $B E$ perpendicular to $O B$
$P Q$ and $B E$ intersect at the point $R$
5. $R P$ and $R B$ are the required tangents
6. The measurement of $O R$ is 8 cm

Justification:
PR is the tangent to a circle

$$
\angle O P Q=900
$$

$B R$ is the tangent to a circle

$$
\angle O B R=900
$$
So we get

$$
\angle P O B=180-60=1200
$$
In BOPR

$$
\angle B R P=360-(120+90+90)=600
$$
Therefore, the distance between the centre of the circle and the point of intersection of tangents is 8 cm.

Posted by

infoexpert27

View full answer

Similar Questions

Latest Question