Question

In the following diagram, QR is tangent to circle P. Which of the following could be the missing side lengths? Select all that apply. (3 answers)
A. 8 and $4\sqrt{3}$
B. 2 and $4\sqrt{2}$
C. 3 and 5
D. 2 and $2\sqrt{5}$
E. 6 and 10
Please show your work too

Answer 1

Answer:

QR is tangent to circle P at point Q

=> RQP = 90 deg

=> RQP is right triangle.

=> Applying Pythagorean theorem for right triangle RQP:

    QP^2 + QR^2 = RP^2

=>4^2 + QR^2 = RP^2

=> Option A is correct.

(4^2 + (4*$\sqrt{3}$)^2 = 16 + 48 = 64 = 8^2)

=> Option C is correct.

(4^2 + 3^2 = 16 + 9 = 25 = 5^2)

=> Option D is correct

(4^2 + 2^2 = 16 + 4 = 20 = (2$\sqrt{5}$)^2)

Hope this helps!

:)