Side of pedal triangle and Circum-Radius of pedal Triangle

STATEMENT-1: IFR be the circumradius of a Delta ABC, then circumradius of its excentral Delta I_(1)I_(2)I_(3), is 2R STATEMENT-2: If circumradius of a triangle be R, then circumradius of its pedal triangle ism (R)/(2) .

Pedal Triangle and Ambiguous Case

If the sides of the triangle are the roots of the equation x^(3)-2x^(2)-x-16 =0, then the product of the in-radius and circum-radius of the triangle ,is

6. Let one angle of a triangle be 60°, the area of triangle is 10/3 and perimeter is 20 cm. Ifa>b> c where a, b and e denote lengths of sides opposite to vertices A, B and C respectively, then which of the following is (are) correct? (A) Inradius of triangle is 3 (C ? (B) Length of longest side of triangle is 7 ) Circum radius oftriangle is (D) Radius of largest escribed circle is 12

Find the circum-centre and the circum-radius of a triangle ABC formed by the vertices A(2,-2) , B (-1,1) and C(3,1).

The circum-radius of an equilateral triangle is 8 cm. The in-radius of the triangle is

In a triangle the sum of two sides is x and the product of the same two sides is y .If x^(2)-c^(2)=y , where c is the third side of the triangle , then the ratio of the in-radius to the circum-radius of the triangle is

Pedal triangle || Ambiguous case

Find the area, circum-radius and in-radius of the pedal triangle.