How Long is the Tangent to Circle P?

What is the approximate length of RP?

Round to the nearest tenth.

5.6 units

6.1 units

8.3 units

9.8 units

Answer: 6.1 units

Explanation:

Given that R is tangent to circle P at point Q and RQ = 5.3 units while QP = 3 units. We need to find the length of RP.

Since a tangent to a circle is perpendicular to the radius through the point of contact, we know that ∠PQR = 90°.

By applying the Pythagorean theorem in triangle PQR, we can find the length of RP:

Using the formula RP² = RQ² + QP²:

RP² = 5.3² + 3²

RP² = 28.09 + 9

RP² = 37.09

RP = √37.09

RP ≈ 6.1 units (rounding off to the nearest tenth)

Therefore, the approximate length of the tangent RP to circle P is 6.1 units.

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