In a right triangle ABC, a circle with a side. AB as diameter is drawn to intersect the hypotenuse AC in P. Prove that the tangent to the circle at P bisects the side BC.

In the isosceles triangle ABC, AB=AC, if a circle is drawn with the side AB as diamter then the circle intersects the side BC at the point D. When BD=4 cm , find the the length of CD.

In triangleABC , AB=AC. If we draw a circle with diameter AB, the circle intersect BC at D, then BD:CD=?

PR is a diameter of a circle. A tangent is draewn at the point P and a point S is taken on the tangent of the circle is such a way that PR=PS. If RS intersects the circle at the point T., prove that ST =PT.

P is any point on diameter of a circle with centre O.A perpendicular drawn on diameter at the point O intersects the point O intersects the circle at the point Q. Extended QP intersects the circle at the point R.A tangent drawn at the point R intersects extended OP at the point S. Prove theat SP=SR. [GP-X]

In right angled triangle ABC , /_A is a right angle. AD is perpendicular on the hypotenuse BC . Prove that (DeltaABC)/(DeltaACD)=(BC^(2))/(AC^(2)) .

In a right-angled triangle, the area of a square drawn on the hypotenuse is equal to the "…..............." of the areas of the squares drawn on other two sides.

In a isoscles triangle ABC, AB = AC. If we draw a circle with diameter AB, then the circle intersect BC at D. IF BD = 4cm then find the length of CD.

In a right triangle ABC right-angled at B, if P and Q are points on the side AB and AC respectively, then___

The equilateral triangle ABC is inscribed in a circle. If P is any point on the ar BC, then prove that AB=PB+PC .

AB is a diameter and AC is a chord of the circle with centre at Q. the radius parallel to AC intersect the circle at D. Prove that D is the mid-point of the are BC.