contestada

Points N and R both lie on circle O. Line segment RQ is tangent to the circle at point R. Circle O is shown. Line segments O R and O N are radii. A line is drawn to connects points R and N to form chord R N. Point Q is outside of the circle. Lines are drawn from points R and N to point Q to form an isosceles triangle. The lengths of R N and N Q are congruent. The length of O N is 5 and the length of R Q is 5 StartRoot 3 EndRoot. What is the perimeter of triangle RON? 10.0 units 15.0 units 18.7 units 23.7 units

Respuesta :

Answer:

B) 15.0

Step-by-step explanation:

took test

Lanuel

Based on the calculations, the perimeter of triangle RON is equal to 15 units.

Given the following data:

  • Angle ORQ = 90°.
  • Side OR (radius) = 5.
  • Side RQ = 5√3.

How to calculate the perimeter of a triangle.

Mathematically, the perimeter of a triangle is given by this formula:

[tex]P = a + b + c[/tex]

Where:

  • a, b, and c are length of sides.

Based on the diagram, we can deduce that side OQ is larger than RQ, thereby, making it a special right-angled triangle with 90-60-30 degree. Thus, side OQ have a length of 10 units and angle QOR is equal to 60°, while angle OQR is equal to 30°.

For the chord length:

[tex]Chord =2rsin(\frac{c}{2} )\\\\Chord =2\times 5 \times sin(\frac{60}{2} )\\\\Chord =10 \times sin30\\\\Chord =10 \times 0.5[/tex]

Chord = 5 units.

For the perimeter of triangle RON:

[tex]Perimeter = ON+OR+RN\\\\Perimeter = 5+5+5[/tex]

Perimeter = 15 units.

Read more on perimeter of a triangle here: https://brainly.com/question/24382052

Ver imagen Lanuel

Otras preguntas