Disegna una circonferenza di diametro \( A B \) e fissa su di essa un punto C. Congiungendo gli estremi del diametro con il punto C si ot- tiene un triangolo rettangolo. Calcola il peri- metro e l'area di tale triangolo se la somma dei cateti è 112 dm e uno è \( \frac{3}{4} \) dell'altro. \[ \left[192 \mathrm{dm} ; 1536 \mathrm{dm}^{2}\right] \]

(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 \( =\ldots . . . . . . . \mathrm{cm} \). \( \begin{array}{llll}81 & \text { (b) } 9 & \text { (c) } \sqrt{963} & \text { (d) } 18\end{array} \)

यदि एक समांतर चतुर्भुज \( A B C D \) के बिंदुओं \( A, B \) तथा \( C \) के निर्देशांक क्रमश: \( (1,2),(3,4) \) तथा \( (2,5) \) है, तो विकर्ण \( A D \) का समीकरण है [JEE (Main) 2019] \( \begin{array}{ll}\text { (a) } 5 x+3 y-11=0 & \text { (b) } 3 x-5 y+7=0 \\ \text { (c) } 3 x+5 y-13=0 & \text { (d) } 5 x-3 y+1=0\end{array} \)

4) Base perimeter of a square pyramid is 40 cm and height 30 cm a) What is the base area? b) Find the volume of the pyramid Answer any four questions. Each carries 3 scores Draw a circle of radius 3 cm . Mark a pointP on the circle. Construct tangent to the

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

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.