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 an equilateral triangle show that the in-radius and the circum-radius are connected by r =R/2.

In a Delta ABC, 2s= perimeter and R = circumradius. Then, find s/R.

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

In an equilateral triangle with usual notations the value of (27r^(2)R)/(r_(1)r_(2)r_(3)) is equal to

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

In triangle ABC, let angle C = pi//2 . If r is the inradius and R is circumradius of the triangle, then 2(r + R) is equal to

If R_(1) is the circumradius of the pedal triangle of a given triangle ABC, and R_(2) is the circumradius of the pedal triangle of the pedal triangle formed, and so on R_(3), R_(4) ..., then the value of sum_( i=1)^(oo) R_(i) , where R (circumradius) of DeltaABC is 5 is

In an acute angled triangle A B C , a semicircle with radius r_a is constructed with its base on BC and tangent to the other two sides. r_b a n dr_c are defined similarly. If r is the radius of the incircle of triangle ABC then prove that 2/r=1/(r_a)+1/(r_b)+1/(r_c)dot

Let ABC be a triangle having O and I as its circumcentre and incentre, respectively. If R and r are the circumradius and the inradius respectively, then prove that (IO) 2 =R 2 −2Rr. Further show that the triangle BIO is right angled triangle if and only if b is the arithmetic mean of a and c.

ln a triangle with sides a, b, c if r1 gt r2 gt r3 (which are the ex-radii), then