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

A semicircle is inscribed inside a rectangle in such a way, so that the diameter semicides with the length of the rectangle. If the area of the semicircle is 50pi , then what is area of the rectangle? (a)200 (b)175 (c)150 (d)125

Let a<=b<=c be the lengths of the sides of a triangle.If a^(2)+b^(2)

In a triangle with sides, a,b, and c a semicircle toughing the sides AC and CB is inscribed whose diameter lies on AB. Then the radius of the semicricel is

PQ is a vertical tower having P as the foot. A,B,C are three points in the horizontal plane through P. The angles of elevation of Q from A,B,C are equal and each is equal to theta . The sides of the triangle ABC are a,b,c, and area of the triangle ABC is . Then prove that the height of the tower is (abc) tantheta/(4)dot

A right angle triangle whose hypotenuse is c and its perpendicular sides are a and b. Three semicircles are drawn along the three sides of this triangle in such a way that the diameter of each semicircle is equal to the length of the respective side of the triangle. The semicircle drawn wiht the help of hypotenuse intersects the other two semicircles as shown in the concerned diagram. Find the area of the shaded region.

AB is the diameter of a semicircle k,C is an arbitrary point on the semicicle other than A or B and S is the centre of the circle inscribed into triangle ABC, then measure of-