Question

24.In the given figure 0 is the centre of the circle and ZDAB = 50°,Find x® and yo.
D
yoda
A500

Answer 1

Given:

A circle with O as a centre and a ∠DAB=50°

To find :

The value of  x° and y°

Solution:

Let the radius of circle = r

Then in Δ OAB

$\because$ OA = OB = r

$\therefore$  $\angle\,OBA=\angle\,OAB =50^{\circ}$

$\therefore \angle AOB +50+50=180^\circ\\\\\therefore \angle AOB = 180-100=80^\circ$

Now  at point O

x + 80° = 180° ( As AOD is a straight line)

∠x = 180-80= 100°

Now ABCD is a cyclic quadrilateral

$\therefore \angle x +\angle y =180^\circ \\\\\angle y = 180-\angle x\\\\=180-100\\\\ = 80^\circ$

Answer:

$\angle x= 100^\circ\\\\\\\angle y= 80^\circ$

Concept used:

1. All the line drawn from centre of circle to its circumference are equal to radius r
2. Opposite angles of a cyclic quadrilateral are supplementary
3. In a triangle angles opposite to equal sides are equal

Other important concepts:

1. The length of the tangents drawn from an external point to same circle are equal
2. The perpendicular drawn from centre to a chord bisects the chord.