If `I_1, I_2, I_3` are the centers of escribed circles of ` A B C ,` show that are of ` I_1I_2I_3=(a b c)/(2r)dot`

If 1 is the incentre and I_1,I_2,I_3 are the centre of escribed circles of the triangleABC . Prove that II_(1)^(2)+I_2I_(3)^(2)= II_(2)^(2)+I_(3)I_(1)^(2)= I_(1)I_(2)^(2)+II_(3)^(2)

If I is the incenter of A B Ca n dR_1, R_2,a n dR_3 re, respectively, the radii of the circumcircles of the triangles I B C ,I C Aa n dI A B , then prove that R_1R_2R_3=2r R^2dot

A semicircular ring has mass m and radius R as shown in figure. Let I_(1),I_(2),I_(3) and I_(4) be the moments of inertia of the four axes as shown. Axis 1 passes through centre and is perpendicular to plane of ring. Then, match the following columns. {:(,"Column-I",,"Column-II"),("(A)",I_(1),"(p)",(mR^(2))/(2)),("(B)",I_(2),"(q)",(3//2)mR^(2)),("(C)",I_(3),"(r)",mR^(2)),("(D)",I_(4),"(s)","Data is insufficient"):}

The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the center O and perpendicular to the plane of the plate is ( i ) I_(1)+I_(2) ( ii ) I_(2)+I_(4) ( iii ) I_(1)+I_(3) ( iv ) I_(1)+I_(2)+I_(3)+I_(4) where I_(1) , I_(2) , I_(3) and I_(4) are repectively moments of inertia about axes 1 , 2 , 3 and 4 which are in the plane of the plane

Find the Radius of escribed circle (i) r1= Delta /(s-a)=s tan A/2=4R sin A/2cos B/2cos C/2

If A^(2)-A+I=0, then the inverse of A is: (A) A+I (B) A(C)A-I (D) I-A