From an external point P, at a distance of 7 cm from the centre of a circle of radius 3 - Maths - Constructions

Question

From an external point P, at a distance of
7 cm from the centre of a circle of radius
3 cm , construct one tangent PQ to the
circle At the end point R of the diameter through
Q, construct a tangent to the circle

Ashutosh Verma · Accepted Answer

Answer :

We follow these steps :

Step 1 : Draw a line OP = 7 cm

Step 2 : Take radius of 3 cm and center " O " draw a circle

Step 3 : Take any radius ( More than half of OP ) and center " O "
and " P " draw two arcs from both pont on both side of line OP
These arcs intersect at " A " and " B " Join AB, line AB intersect
line OP at " C "

Step 4 : Take radius of ( CP = OC ) and center " C :" draw a
semicircle that intersect our circle with center " O " at " Q " and
" I "

Step 5 : Join PQ we get our tangent , Now we draw diameter from
point " Q " that meet at " R " of circumference of circle

Step 6 : Take any radius ( Less than half of OR ) and center " R :
draw a semicircle that intersect line OR at D Now with sane radius
and center " D " draw an arc that intersect our semicircle at " E "
Again with sane radius and center " E " draw an arc that intersect
our semicircle at " F " Now with sane radius and center " E " and "
F "draw arcs these arcs intersect at " G "

Step 7 : JOin RG and extend it to " H " we get tangent RH

From an external point P, at a distance of 7 cm from the centre of a circle of radius 3 cm , construct one tangent PQ to the circle. At the end point R of the diameter through Q, construct a tangent to the circle.