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R is tangent to circle P at point Q.

What is the approximate length of RP? Round to the nearest tenth.
5.6 units
6.1 units
8.3 units
9.8 units

1 Answer

6 votes

Answer: 6.1 units

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.

User ShazSimple
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