PQ is a lines segment and `R` is its midpoint. Semicircles are drawn at the same side of `PQ` taking `PR, RQ and PQ` as diameters. A circle of radius `r` and centre `O` is drawn touching all the three semi circles.
Prove that ` r = (1)/(6) PQ`

In the figure semicircles are drawn with PQ, PB and BQ as diameter. PB = BQ = 21 cm . A circle with centre O is drawn to touch all the three semicircles. Find its radius and also find the shaded region.

AB is a line segment of length 2a with M as mid-point. Semicircles are drawn on one side with AM, MB and AB as diameter as shown in the above figure. A circle .with centre O and radius r is drawn such that this circle touches all the three semicircles. The value of r is

PQ is a line segment 12cm long and R is a point in its interior such PR=8cm,then

PQ is a lines segment of 12 cm whose midpoint is R. Taking PR, RQ and PQ as diameters semicircles are drawn at the same side of PQ. The area of the circle that touches all the three circles is

In the given figure, AB is a line of length 2a and mid Point M. Taking AM, MB and AB as diameters semi circles are drawn on the same sides of the line. Taking centre O and radius 'r' a circle is drawn such that it touches all the three circles. Then find the value of r.

PS is the diameter of a circle of radius 6cm. The points Q and R cts the diameter Ps.Semi circles are drawn on PQ and Qs as diameters. Find the area of the shaded region.

Let PQ and RS be tangent at the extremities of the diameter PR of a circle of radius r. If P S and RQ intersect at a point X on the circumference of the circle,then prove that 2r=sqrt(PQ xx RS).

If Figure-1, from an external point P, two tangents PQ and PR are drawn to a circle of radius 4 cm with centre O. if angleQPR=90^(@) , then length of PQ is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle,then 2r equals