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.