Question

in the given figure ,tangents pq and pr drawn from an external point p to a circle with centre o , such that angle rpq=30. a chord rs is drawn parallel to tangent pq find angle rqs​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given: In the given figure ,tangents PQ and PR drawn from an external point P to a circle with centre O, such that angle RPQ=30°. A chord RS is drawn parallel to tangent PQ.

To find: find angle RQS.

Solution:

Step1:See figure 1

We know that radius of circle makes 90° angle with the intersection of tangent.

Now,PROQ is a Quadrilateral,thus from angle sum property of Quadrilateral $\angle QOR=150°$

Step 2: See figure 2

As RS is parallel to PQ,here QR is a transversal thus,

$\angle PQR=\angle QRS$

[Alternate interior angles]

From tangent property,we know that PQ=PR

thus, ∆PQR is isosceles triangle,According to property of isosceles triangle $\angle PQR=75°$

Thus,

$\angle QRS=75°$

Step 3: See figure 3

We know that the angle subtended by a chord at centre of circle doubles the angle subtended by same chord at the segment of circle.

Chord QR subtends 150° at centre thus it subtends 75° to the remaining segment.

Thus,

$\angle QSR=75°$

Step 4: See figure 4

Apply angle sum property of triangle

$\angle QRS+\angle QSR+ \angle RQS=180°$

$\angle RQS=180°-150°$

$\angle RQS=30°$

Final answer:

$\angle RQS=30°$

Hope it helps you.

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