**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 drawn
- 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:- **

- 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.

Subjects |
Maths (Part-1) by Mr. M. P. Keshari |

Chapter 9 |
Circle |

Chapter 10 |
Tangents to a circle |

Chapter 11 |
Geometrical Construction |

Chapter 12 |
Troigonometry |

Chapter 13 |
Height and Distance |

Chapter 14 |
Mensuration |

Chapter 15 |
Statistics |

Chapter 16 |
Probability |

Chapter 17 |
Co-ordinate Geometry |