Point p is the center of two concentric circle pq =2.5 and ps= 5 rs is tangent to the smaller circle and a chord of the larger circle what is length of rs to the nearest tenth

Here Q and S are the points on smaller and larger circles respectively and P is the center of both circles.

Given that, radius of smaller circle, PQ= 2.5

and radius of larger circle, PS= 5

RS is a chord of the larger circle and tangent to the smaller circle at point Q.

That's why, ∠PQS will be 90° and the ΔPQS is a right angle triangle.

For ΔPQS, we will use Pythagorean Theorem, according to this theorem here:

(PS)² = (PQ)² + (QS)²

⇒ (5)² = (2.5)² + (QS)² [By plugging PS= 5 and PQ= 2.5]

⇒ 25 = 6.25 + (QS)²

⇒ 18.75 = (QS)² [Subtracting 6.25 from both sides]

⇒ QS = √18.75

⇒ QS = 4.3301

Here Q is the midpoint of the cord RS, so RQ= QS

That means, RS = 2× QS

= 2× 4.3301

= 8.6602

= 8.7 [Rounding to the nearest tenth]

So, the length of RS to the nearest tenth is 8.7

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