Question

In a given figure PQ and PR are tangents to the circle with centre O such that angle QPR=50 Degree.Find angle OQR

Answer 1

hope it helps you.......

Answer 2

The angle OQR is 25°.

Given:

Angle QPR=50°

To find:

Angle OQR

Solution:

The radius is perpendicular to the given tangents PQ and PR.

Angle OQP=Angle ORP=90°

In quadrilateral PROQ,

Angle OQP+Angle ORP+angle QPR+Angle ROQ=360°

Using values,

90°+90°+50°+angle ROQ=360°

Angle ROQ+360°-230°

Angle ROQ=130°

Now, in ΔQOR,

OQ=OR (circle's radius)

So, angle OQR=angle ORQ

Angle OQR+Angle ORQ+angle ROQ=180°

2(Angle OQR)+130°=180°

2(Angle OQR)=180°-130°

2(Angle OQR)=50°

Angle OQR=50°/2

Angle OQR=25°

Therefore, the angle OQR is 25°.