JEE Advance - Mathematics (1979 - No. 23)
(b) If a triangle is inscribed in a circle, then the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex. Prove the above statement.
The diameter of the inscribed circle in a right-angled triangle ABC (right-angled at B) is equal to AB + BC - AC.
If a triangle is inscribed in a circle, the product of any two sides is equal to the product of the radius and the perpendicular distance of the third side from the opposite vertex.
If a triangle is inscribed in a circle, the product of any two sides is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex.
The area of the right-angled triangle ABC is equal to (AB * BC)/2.
The radius of the inscribed circle in any triangle is equal to the area of the triangle divided by its semi-perimeter.