In a right triangle in which , a circle is drawn with as diameter intersecting the hypotenuse at . Prove that the tangent to the circle at bisects .
Step 1: Drawing the diagram
Given: is the diameter of the circle.
and are tangents drawn from an external point .
Let's draw the figure.
From the figure,
………… [ Length of tangents drawn from an external point to the circle are equal ]
[ In a triangle, equal sides have equal angles opposite to them ]
[ Angle in a semi-circle is right angle ]
[ Linear pair ]
Step 2: Prove the statement
In
[ Angle sum property ]
……………
Now,
……………
From, equation and equation , we get
In
……………
From, equation and equation , we get
Thus, the tangent at bisects the side