QR is tangent to circle P at point Q.
Circle P is shown. Line segment P Q is a radius. Line segment Q R is a tangent that intersects the circle at point Q. A line is drawn from point R to point P and goes through a point on the circle. The length of R Q is 5.3 and the length of Q P is 3.
What is the approximate length of RP? Round to the nearest tenth.
Answers
If the tangent RQ = 5.3 and the radius PQ = 3 then the approximate length of RP is 6.1.
Step-by-step explanation:
It is given,
QR is a tangent to the circle touching the circle at point Q and the length of RQ = 5.3
The length of the radius of the circle, QP = 3
Since a tangent to a circle is perpendicular to the radius through the point of contact, therefore,
∠PQR = 90°
Now referring to the figure attached below, and by using Pythagoras theorem, in ∆ PQR, we get
RP² = RQ² + QP²
⇒ RP² = 5.3² + 3²….. [substituting the given values]
⇒ RP = √[5.3² + 3²]
⇒ RP = √[28.09 + 9]
⇒ RP = √[37.09]
⇒ RP = 6.0901
⇒ RP = 6.1 …… [rounding off to its nearest tenth]
Thus, the approximate length of the RP is 6.1.
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The length of RP is 6.1 unit.
Step-by-step explanation:
Consider the provided information.
QR is a tangent to a circle with centre P touching the circle at Q.
Consider the figure shown below:
A line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
The triangle is a right angle triangle, where PQ and QR are the legs of the triangle and we need to find hypotenuse RP of the triangle.
By using the Pythagoras theorem:
Hence, the length of RP is 6.1 unit.
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