Question

PA and PB are tangent to circle O. PA is equal to the radius of the circle. What kind of quadrilateral is PAOB? Explain.

Answer 1

Answer:

Hence The PAOB is Square Quadrilateral.

Step-by-step 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)