solvi i seguenti esercizi sul punto medio. Dato un segmento \( A B \) che misura 14 cm , con- sidera il segmento \( C D \) di 7 cm adiacente ad \( A B \) con \( B \equiv C \). Trova il punto medio del segmento somma.

Vhat is the area of the circular ring included between two concentri irclec of radius 14 cm and 10.5 cm ?

(27) If the distance between the point and the center of a circle \( =15 \mathrm{~cm} \). and the power of this point with respect to the circle \( =144 \mathrm{~cm}^{2} \), then the radius length of the circle \( =\ldots . . . . . . . \mathrm{cm} \). \( \begin{array}{llll}81 & \text { (b) } 9 & \text { (c) } \sqrt{963} & \text { (d) } 18\end{array} \)

A circle whose centre \( (-2,5) \) passes through point \( P(10,10) \). Find the equation of the is the form of \( a x^{2}+b y^{2}+c x+d y+k=0 \). Where ab, c \( d \) and \( k \) are constants.

Given the equations of lines \( \boldsymbol{l}_{1} \) and \( \boldsymbol{l}_{2} \) are \( \mathrm{r}=(\mathrm{i}+2 \mathrm{j}+3 \mathrm{k})+\lambda(\mathrm{i}-\mathrm{j}+2 \mathrm{k}) \) and \( \mathrm{r}=(5 \mathrm{i}+\mathrm{j}+5 \mathrm{k})+\mu 2 \mathrm{i}+\mathrm{j}-2 \mathrm{k}) \) respectively, where \( \lambda \) and \( \mu \) are real patameters. (a) Show that lines \( \boldsymbol{\ell}_{1} \) and \( \boldsymbol{\ell}_{2} \) intersect and hence, state the coordinates of the point of intersection. (b) Find the Cartesian equation of the plane \( \Pi_{1} \), which contains lines \( \boldsymbol{\ell}_{1} \) and \( \boldsymbol{\ell}_{2} \). (c) The planes \( \Pi_{2} \) and \( \Pi_{3} \) are with equations \( 2 \mathrm{r}+2 \mathrm{y}+z=3 \) and \( 2 \mathrm{r}+p y+2 z=2 \) respectively, where \( p \) is a constant. (i) Find the vector equation of the line of intersection between planes \( \Pi_{1} \) and \( \Pi_{2} \). (ii) Determine the value of \( p \) such that the planes \( \Pi_{1}, \Pi_{2} \) and \( \Pi_{3} \) do not have any common point.

(c) The planes \( \Pi_{2} \) and \( \Pi_{3} \) are with equations \( \left.2 x+2 y+1\right) \) respectively, where \( p \) is a constant. (i) Find the vector equation of the line of intersection between planes \( \Pi_{1} \) and \( \Pi_{2} \). (ii) Determine the value of \( p \) such that the planes \( \Pi_{1}, \Pi_{2} \) and \( \Pi_{3} \) do not have any common point.