Answer:
Hence The PAOB is Square Quadrilateral.
Explanation:
Given:
PA and PB are two tangents to circle with center O
And PA =radius of circle.
To Find:
What kind of Quadrilateral PAOB is ?
Solution:
consider a circle with center O and radius r
Here PA and PB are tangent to circle hence they will meet at one point on the circle .
So join those points with center of circle
Now Constructing the figure as per given data we get ,
By Applying,
the theorem of two tangent that if we draw to tangent to a circle which meet at external point of circle here as 'P' then they are congruent .
Given that
PA=radius of circle=r
But by theorem PA=PB
Hence PB=r
So All the length of quadrilateral are equal.
Now for angle Draw a line From P to center of circle which gives two triangles
Now Consider two triangle PAO and PBO
as PA=OA there
PAO is isosceles triangle i.e 45-45-90 triangle
Similar for PBO is isosceles triangle i.e 45-45-90 triangle
Therefore angle
APB=90 degree and angle made by tangent on circle are 90 degree
So,
Remaining angle at center of circle will be also 90 degree
Hence The PAOB is Square Quadrilateral.
(Refer the attachment)