In ` A B C ,` as semicircle is inscribed, which lies on the side `cdot` If `x` is the lengthof the angle bisector through angle `C ,` then prove that the radius of the semicircle is `xsin(C/2)dot`

In a ΔABC, a semicircle is inscribed, whose diameter lies on the side c. Then find the radius of the semicircle.(Where Δ is the area of the triangle ABC)

Let alt=blt=c be the lengths of the sides of a triangle. If a^2+b^2 < c^2, then prove that triangle is obtuse angled .

In a triangle with sides a, b and c a semicircle touching the sides AC and CB is inscribed whose diameter lies on AB. Then , the radlus of the semicircle is:

If A,B,C are the angles of a triangle, prove that the maximum value of cos A cos B cos C "is" (1)/(8)

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

If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b^2=a^2+2ac dot

If A ,B ,a n dC are three points on the hyperbola x y=c^2 such that A B subtends a right angle at C , then prove that A B is parallel to the normal to the hyperbola at point Cdot

A circle of radius 4cm is inscribed in A B C , which touches the side B C a t Ddot If B D=6c m ,D C=8c m then (a) the triangle is necessarily acute angled (b) tan(A/2)=4/7 (c) perimeter of the triangle A B C is 42c m (d) area of A B C is 84c m^2

If A, B, C are the angles of a triangle then tan ((B+C)/2)=

The sides of a triangle are x^2+x+1,2x+1,a n dx^2-1 . Prove that the greatest angle is 120^0dot