Question

1. In the diagram shown, BC is tangent to circle A at point C. If AB = 17 and BC =15, then which of the
following is the length of the radius of circle A?
(1) 6
(2) 8
(3) 10
(4) 12

Answer 1

The length of radius of circle A is 8, If BC is tangent to circle A at point C and AB = 17 and BC =15.

Step-by-step explanation:

The given is,

                   BC is tangent to circle A at point C

                   AB = 17

                   BC =15

Step:1

             From the diagram,

             Tangent to the circle at a certain point and connected with center of circle, it makes right angle triangle.

             So, ABC is a right angled triangle,

            By Pythagorean theorem,

                          $Hypotenuse^{2} = Side^{2} +Side^{2}$......................(1)

            For the Triangle ABC,

                          $AB^{2} = AC^{2} + BC ^{2}$.......................................(2)

            From given values,

                          AB = 17

                          BC = 15

           Equation (2) becomes,

                       $17^{2} = AC^{2} + 15^{2}$

                       $289=AC^{2} + 225$

                     $AC^{2} = 289-225$

                     $AC^{2} = 64$

           Take root on both sides,

                        AC = $\sqrt{64}$

                        AC = 8

           Where, AC = Radius of circle = 8

Result:

           The length of radius of circle A is 8, If BC is tangent to circle A at point C and AB = 17 and BC =15.

Answer 2

Radius of the circle A on which BC is tangent to the circle at point C from external point B is 8 units.

How to find the side of a right angle triangle?

To find the side of a right angle triangle, the Pythagoras theorem is used.

Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.

In the diagram shown, BC is tangent to circle A at point C. If AB = 17 and BC =15.

Draw a line from A to point C. This line segment AC is the radius of the circle which is perpendicular to the tangent BC.

Now in the right angle triangle ACB, the length of AC is found out using the Pythagoras theorem as,

$(AB)^2=(AC)^2+(BC)^2\\17^2=(AC)^2+15^2\\(AC)^2=17^2-15^2\\(AC)^2=289-225\\AC=\sqrt{64}\\AC=8$

AC is the radius of the circle. Hence, the length of the radius of the circle A on which BC is tangent to the circle at point C from external point B is 8 units.

Learn more about the Pythagoras theorem here;

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