In a right-triangle ABC in which `angleB=90^(@)`, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P. Prove that the tangent to the circle at P bisects BC.

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.

ABC is a right triangle in which angleA = 90^(@) and AB = AC. Find angleB and angleC .

In the given figure, two circles touch each other externally at the point C. Prove that the common tangent to the circle at C bisects the common tangents at P and Q.

ABC and ADC are two right triangle with common hypotenuse AC. Prove that CAD = CBD.

ABC is right angled triangle in which /_ A = 90^(@) and AB = AC. Find B and C.

In the figure, an isosceles triangle ABC with AB=AC circumscribes a circle. Prove that the point of contact P bisects the base BC.

In the fig.ABC is a quadrant of a circle of radius 14cm and a semicircle is drawn with BC as a diameter. Find the area of the shaded region.

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of DeltaPQR is double the perimeter of DeltaABC.

Let ABC be a right triangle in which AB=6cm, BC=8cm and /_B=90^(@) . BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side.