If `(m_i , 1/m_i), i= 1, 2, 3, 4` are four distinct points on a circle, show that `m_1 m_2 m_3 m_4 = 1`

If (m_(i),1/(m_(i))),m_(i)gt0,i=1,2,3,4 are four distinct points on a circle, show that m_(1)m_(2)m_(3)m_(4)=1 .

If (m_i,1/m_i),i=1,2,3,4 are concyclic points then the value of m_1m_2m_3m_4 is

If (m_(i),1//m_(i)), i=1,2,3,4 are concyclic points, then the value of m_(1)m_(2)m_(3)m_(4)" is"

ABCD is a square of length a, a in N , a > 1. Let L_1, L_2 , L_3... be points on BC such that BL_1 = L_1 L_2 = L_2 L_3 = .... 1 and M_1,M_2 , M_3,.... be points on CD such that CM_1 = M_1M_2= M_2 M_3=... = 1 . Then sum_(n = 1)^(a-1) ((AL_n)^2 + (L_n M_n)^2) is equal to :

Let l_i,m_i,n_i; i=1,2,3 be the direction cosines of three mutually perpendicular vectors in space. Show that AA'=I_3 where A=[[l_1,m_1,n_1] , [l_2,m_2,n_2] , [l_3,m_3,n_3]]

Four paticle of masses m_1 = 2 m, m_2 = 4 m, m_3 = m and m_4 are placed at four corners of a square. What should be the value of m_4 so that the centres of mass of all the four particle are exactly at the centre of the square ?

If m_1 =10kg, m_2 = 4kg and m_3 = 2kg the tension in the string connecting m_1 and m_2 is,

Prove that a point can be found which is at the same distance from each of the four points : (a m_1, a/(m_1)), (a m_2, a/(m_2)),(a m_3, a/(m_3))"and"(a/(m_1m_2 m_3), a m_1m_2m_3)

Prove that (-a,-a/2) is the orthocentre of the triangle formed by the lines y = m_(i) x + a/(m_(i)) , I = 1,2,3, m_(1) m_(2) m_(3) being the roots of the equation x^(3) - 3x^(2) + 2 = 0

Show that the lines y-m_1 x-c_1 = 0 , y-m_2x-c_2 = 0 and y-m_3 x-c_3 =0 form an isosceles triangle with the first line as base if : (1+m_1 m_2) (m_1 - m_3) + (1+m_1 m_3) (m_1 - m_2) = 0