If from an extrenal point B of a circle with centre 0, two tangents BC and BD are drawn such that `angleDBC=120^(@)`, prove that `BC+BD=BO` i.e., BO=2BC.

Two tangent segments BC and BD are drawn to a circle with centre O and radius r such that angleDBC=120^(@) . Prove that BO=2BC.

ABC is an isosceles triangle with AB=AC and D is a pooint on AC such that BC^(2)=ACxCD .Prove that BD=BC

ABC is a triangle in which AB=AC and D is a point on AC such that BC^(2)=AC xx CD .Prove that BD=BC .

In Figure,AD=AE and D and E are points on BC such that BD=EC .Prove that AB=AC

In the adjoining figure, BC is a diameter of the circle with centre M. PA is a tangent at A from P, which is a point on line BC. AD bot BC prove that DP^(2)=BPxxCP-BDxxCD

In an equilateral triangle ABC,D is a point on side BC such that BD=(1)/(3)BC Prove that 9AD^(2)=7AB^(2)

In /_ABC,AB=AC and D is any point on BC , prove that AB^(2)-AD^(2)=BD.CD

In the figure,O is the center of the circle and BO is the bisector of angle ABC show that AB=BC