Question

If PQ is a chord of a circle with radius r units and R is a point on the circle such that angle PRQ=90 degree,then find the length of PQ

Answer 1

Given:-

• ∠PRQ = 90°

• PQ is a cord.

• Radius of circle is " r " units.

To Find:-

• Length of chord PQ

Solution:-

Here, PQ is the chord and R is a point on the circle.

So, It is given that ∠PRQ = 90°

And, We know the theorem that "Angle formed in a semicircle is of 90°".

So, Chord PQ will be diameter so that it will form a right angle at point R in a semicircle.

∵ Radius of circle is r units

∴ Diameter of circle will be 2r units

And, PQ is a diameter of the circle.

Hence, PQ = 2r units.

Some Important terms:-

• “Two equal chords of a circle subtend equal angles at the center of the circle.”

• “The perpendicular to a chord bisects the chord if drawn from the center of the circle.”

• “Equal chords of a circle are equidistant (equal distance) from the center of the circle.”

• “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”

Answer 2

Answer:

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Step-by-step explanation:

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