In Fig. 4.237, `L M=L N=46o` . Express `x` in terms of `a ,\ b` and `c` where `a ,\ b ,\ c` are lengths of `L M ,\ M N` and `N K` respectively. (FIGURE)

In figure, sides L M and L N of L M N are extended to P and Q respectively. If x > y , show that L M > L N .

In Figure, sides L M\ a n d\ L N OF /_\ LMN are extended to P\ a n d\ Q respectively. If x > y , show that L M > L N .

If l ,\ m,\n are three lines such that l || m\ a n d\ n_|_l , prove that n_|_mdot

In Figure, P A and P B are tangents from an external point P to a circle with centre O . L N touches the circle at M . Prove that P L+L M=P N+M N .

In the measurement of a physical quantity (L), the formula used is L=k(m xx n) , where k is a constant and m and n are the quantities to be measured. If the % errors in m and n are respectively 3% and 5%. The % error in the measurement of L is

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ L O B)=a r\ (\ M O C) .

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

In Figure, A D is a median and B L ,\ C M are perpendiculars drawn from B\ a n d\ C respectively on A D\ a n d\ A D produced. Prove that B L=C M

Let ABC be a triangle inscribed in a circle and let l_(a)=(m_(a))/(M_(a)), l_(b)=(m_(b))/(M_(b)), l_(c )=(m_(c ))/(M_(c )) where m_(a), m_(b), m_(c ) are the lengths of the angle bisectors of angles A, B and C respectively , internal to the triangle and M_(a), M_(b) and M_(c ) are the lengths of these internal angle bisectors extended until they meet the circumcircle. Q. The minimum value of the expression (l_(a))/(sin^(2)A)+(l_(b))/(sin^(2)B)+(l_(c ))/(sin^(2)C) is :