If `H` is the orthocentre of triangle `A B C ,R=` circumradius and`P=A H+B H+C H` , then (a) `P=2(R+r)` (b) `max of P is 3R` (c) `min of P is 3R` (d) `P=2(R-r)`

If H is the orthocentre of triangle ABC, R = circumradius and P = AH + BH + CH , then

If H is the orthocentre of a triangle ABC, then the radii of the circle circumscribing the triangles B H C ,C H Aa n dA H B are respectively equal to: a, R,R,R b. sqrt(2)R ,sqrt(2)R ,sqrt(2)R c. 2R ,2R ,2R d. R/2, R/2, R/2

If Delta P Q R\ ~= Delta E F D , then /_E= (a) /_P (b) /_Q (c) /_R (d) None of these

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to (a) a+b (b) b+c (c) c+a (d) a+b+c

In triangle A B C , let /_c=pi/2dot If r is the inradius and R is circumradius of the triangle, then 2(r+R) is equal to a+b (b) b+c c+a (d) a+b+c

The radii r_1, r_2,r_3 of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m^2a n d its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

Consider a D E F , the pedal triangle of the A B C such that A-F-B\ a n d\ \ B-D-C are collinear. If H is the incentre of D E F and R_1,\ R_2,\ R_3 are the circumradii of the quadarilaterals A F H E ; B D H F\ a n d\ C E H D respectively, then prove that sumR_1=R+r where R is the circumradius and r is the inradius of A B Cdot

In an equilateral triangle, the inradius and the circumradius are connected by r=4R b. r=R//2 c. r=R//3 d. none of these

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)

A B C is an equilateral triangle of side 4c mdot If R , r, a n d,h are the circumradius, inradius, and altitude, respectively, then (R+r)/h is equal to (a) 4 (b) 2 (c) 1 (d) 3