Question

AB is a diameter of a circle with centre O. A line drawn through the point A intersects the
circle at the point C and the tangent through B at the point D. Let us prove that
(1) BD2 = AD.DC (ii) The area of the rectangle formed by AC and AD for any straight line
is always equal.​

Answer 1

Answer:

Very easy question banao tum ban jaayega koshish karo

Answer 2

Answer:

From Triangle ABD and angle BCD

Angle ABD=angle BCD

Now,

angle BDC=90°- angle DBC

Therefore, triangle ABD ~triangle BCD

Therefore, BD/AD=DC/BD

or, AD.DC=BD^2[(i) proved]

From triangle ABD and triangle ABC

angle ABD=angle ACB

angle ADB=90°-angle DBC

=angle ABC

Therefore, triangle ABD~ triangle ABC

Therefore, AB/AC=AD/AB

or, AB^2=AC.AD

Therefore, the area of the rectangle formed by AC and AD for any straight line is always equal.