Chapter 11 : Geometrical Construction

Construction 1. To construct a tangent to a circle at a point P on it without using the centre of the circle.

Procedure: -

1. A chord PQ through P is drawn.
2. Any point R is taken on the major arc PQ. PR and QR are joined.
3. 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:-

1. OP is joined and is bisected at M.
2. Taking M as centre and MO as radius a semicircle is drawn which intersect the given circle at Q.
3. 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:-

1. A secant PAB to the circle is drawn.
2. PB is bisected at M.
3. Taking M as a centre and PM as a radius, a semicircle is drawn.
4. Through A is drawn perpendicular to AB which intersect the semicircle at C.
5. Taking P as centre and PC as radius, arcs are drawn to intersect the given circle at Q and R.
6. 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:-

1. Triangle ABC in which BC = a, CA = b and AB = c is constructed.
2. BM and CN is constructed angle bisectors of which intersect at I.
3. is drawn
4. Taking 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:-

1. A triangle ABC is constructed with BC = a, CA = b and AB = c.
2. Perpendicular bisector PQ of BC and RS of CA is constructed. They intersect at O.
3. Taking O as centre and OC as a radius circle is drawn which passes through A, B and C.