Question

any body pls clear my doubt in this qestion that why we cannot say that PORQ is a quadrilateral ​

Answer 1

Answer:

i am giving aal thanks to u itzprince...

Answer 2

Step-by-step explanation:

Given:Figure attached

To find:$\angle PRQ$ and why PORQ is not a Quadrilateral?

Solution:

Why PORQ is not a Quadrilateral ?

Ans: When someone reads the vertices of a triangle;always read in a sequence.

But when we read the vertices of a Quadrilateral we should remember to read in sequential order.

Thus,

here PORQ is not a Quadrilateral(Vertices doesn't follow the sequence here)

But

POQR

OQRP

RPOQ

all are representing the same Quadrilateral.

Showing in attached figure.

Find $\angle PRQ$

We know that, radius of circle makes right angle at the intersection point of tangent.

Here

$\angle OPT=90°$

$\angle QPT=60°$[given]

So,

$\angle OPQ=\angle OPT-\angle QPT$

$\angle OPQ=90°-60°$

$\angle OPQ=30°$

∆POQ is isosceles triangle,because two sides(radius) are equal,thus two opposite angles are also equal.

Thus,

$\angle OQP=30°$

and remaining angle(at centre) will be

$\angle POQ=120°$from angle sum property of triangle.

We know that angle formed by a chord to the center of circle is double of that angle which that chord makes with the segment of circle(which lies behind)

Thus,

$\angle PSQ=60°$

Now,

Quadrilateral PSQR is a cyclic Quadrilateral.

According to the property of cyclic Quadrilateral

$\angle PSQ+ \angle PRQ=180°$

$\angle PRQ=180°-60°$

$\angle PRQ=120°$

Final answer:

$\red{\angle PRQ=120°}$

Hope it helps you.

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