Construction 1. To construct a tangent to a circle at a point P on it without using the centre of the circle.
Procedure: -
- A chord PQ through P is drawn.
- Any point R is taken on the major arc PQ. PR and QR are joined.
- Equal to is constructed.
PX is required tangent to the circle at P.
Construction 2. To construct a tangent to circle from a point P outside the circle using its centre O.
Procedure:-
- OP is joined and is bisected at M.
- Taking M as centre and MO as radius a semicircle is drawn which intersect the given circle at Q.
- PQ is the required tangent from P to the circle.
Construction 3. To construction a tangent to a circle from a point out side the circle without using its centre.
Procedure:-
- A secant PAB to the circle is drawn.
- PB is bisected at M.
- Taking M as a centre and PM as a radius, a semicircle is drawn.
- Through A is drawn perpendicular to AB which intersect the semicircle at C.
- Taking P as centre and PC as radius, arcs are drawn to intersect the given circle at Q and R.
- PQ and PR are joined which is the required tangent.
Construction 4. To construct incircle of a triangle ABC whose sides are BC = a, CA = b and AB = c.
Procedure:-
- Triangle ABC in which BC = a, CA = b and AB = c is constructed.
- BM and CN is constructed angle bisectors of which intersect at I.is drawnTaking I as centre and IL as radius, circle is drawn. This is the required incircle.
Construction 5. To construct a circumcircle of a triangle ABC where a = BC, b = CA and c = AB.
Proceture:-
- A triangle ABC is constructed with BC = a, CA = b and AB = c.
- Perpendicular bisector PQ of BC and RS of CA is constructed. They intersect at O.
- Taking O as centre and OC as a radius circle is drawn which passes through A, B and C.
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