Question

two tangents PQ and PR are drawn from an external point a circle with center 'o' balu said the quadrilateral QORP is a cycle do you agree ? give reason​

Answer 1

Answer:

Step-by-step explanation:

We know that a quadrilateral is cyclic if the sum of its opposite angles is 180.

Now, PQ and PR are tangent, this means that angle PQO=90 and angle PRO=90 Therefore the sum of opposite angle is 180 .So it is cyclic.

Answer 2

QORP is a cyclic quadrilateral.

Step-by-step explanation:

since, OR is the radius and PR is a tangent.

OR  ⊥ PR  

Therefore, $\angle ORP = 90$°

Similarly, OQ  is radius and PQ is tangent

then

$\angle OQP = 90$°

In quadrilateral ORPQ,

Sum of all interior angles = 360º

$\angle ORP +\angle RPQ+\angle PQO +\angle QOR = 360$

90º + RPQ + 90º + QOR = 360º

$\angle O +\angle P = 360-180$

hence,

QORP is a cyclic quadrilateral.

note: In a cyclic quadrilateral, the sum of each pair of opposite angles is 180 degrees. If a quadrilateral has one pair of opposite angles that add to 180, then you know it is cyclic.

#Learn more:

Draw a circle of radius 4cn from a point 10cm from away of the center construct the pair of tangents yo yhe circle and measure the lengt of tangents and wire​

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