Question

O is the centre of the circle. PQ and PR are tangents drawn to the circle. If QPR= 70° then find QOR.

Answer 1

Step-by-step explanation: As,

we know that when a radius touches a tangent at the point of contact the angle formed is always 90°

Therefore,

Angle OQP=Angle ORP=90°

Now,

The sum of angles of a quadrilateral is 360°

OQP+ORP+RPQ+QOR=360°

90+90+46+QOR=360°

QOR=134°

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Answer 2

The angle QOR=110°.

Given:

Angle QPR=70°

To find:

Angle QOR

Solution:

The quadrilateral obtained by joining all the given points is PQOR.

Now, angles ORP and OQP are 90° as they are the radius and are perpendicular to the given tangents.

Now, in quadrilateral PQOR,

Angle QPR+ Angle ORP+ Angle OQP+ Angle QOR=360°

Using the values,

70°+90°+90°+Angle QOR=360°

250°+angle QOR=360°

Angle QOR=360°-250°

Angle QOR=110°

Therefore, the measure of angle QOR is 110°.