Question

class 10th construction show me how to make tangents when centre is not given​

Answer 1

where a Circle is given & its centre is unknown. But we are using the centre, for the construction.And an external point ‘P' is given From this point P we have drawn 2 tangents to the given circle.

First step: by drawing 2 chords & its perpendicular bisectors, wherever they meet is considered as the centre O of the given circle.

Now taking the mid point M of PO, & PM as radius draw a circle, which cuts the given circle at Q & R.

PQ & PR are the required tangents.

JUSTIFICATION: Since PO is the diameter of the circle with centre M.

So, angle PQO =90° ( being an angle on a semi circle)

ie, OQ, which is the radius of the given circle with centre O, is perpendicular to PQ.

Therefore, PQ has to be a tangent to the circle with centre O at Q.

Answer 2

Answer:

M was constructed as the midpoint of OP (See Constructing the perpendicular bisector of a line segment for method and proof) and JM=OM because JM was constructed with compass width set from MO

JM=OM from (1)

JM=MP from (1)

∠JMP and ∠JMO form a linear pair

Substituting (3) and (5) into (6):

(180–2∠MJP) + (180–2∠OJM) = 180

Remove parentheses and subtract 360 from both sides:

–2∠MJP –2∠OJM = –180

Divide through by –2::

∠MJP + ∠OJM = 90

JP is a tangent to O because it touches the circle at J and is at right angles to a radius at the contact point.

(see Tangent to a circle.)

As above but using point K instead of J