Chapter 9 : Circle

Example 4. Triangle ABC is right angled at B. On the side AC, a point D is taken such that AD = DC and AB = BD. Find the measure of

Solution:- The vertices of a right triangle touch a circle with diameter equal to the hypotenuse.

Since AC is the diameter and AD = DC (given)

D is the centre of the circle

AD = DC = BD (radii if the circle given)

But AB = BD (given)

AB = BD = AD --------------------(i)

ABD is an equilateral a triangle

Example 5:- In the adjoining figure, the chord ED is parallel to the diameter AC. Determine .

Solution:- [angles in the same segments]

[Angle is the semi-circle]

In

DE || AC                   (given)

               [Alternate interior angles]