Question

In order for you to answer the question correctly, please use the following three images down below:

(The first part of the question you don't have to worry about because I already did that part for you. All I need is the rest of the second part.)

Explain your reasoning.

Use the equation RQ^2 =(Blank),(Blank) to find (Blank). Then use the (Pythagorean Theorem) to find (Blank)

Please fill in the following blanks above and please show the work on how you got your answer.

(Note-If you can't explain your answer then that's fine. The only thing that I'm asking for is for the work to be shown alongside your answer)

Answer 1

RP; RS; RQ; Pythagorean theorem; PQ

Explanation:

Using segments of secant and tangent theorem:

RQ² = RP × RS to find RQ

RQ² = 26×14

RQ = 2sqrt(91)

Then using pythagoras theorem, find PQ

PR² = PQ² + QR²

26² = PQ² + 364

PQ² = 312

PQ = 2sqrt(78)

Answer 2

RS; RP; RQ; QP

Using RQ^2 = (RS)(RP) <--- That's the length of a secant and chord

to find RQ (You already know the length of RS and RP, because they are labelled, so the only other value that can be found is RQ)

QP (This is the only value that hasn't been found)

(14)(14+12) = RQ^2 -->

14(26) = RQ^2 -->

2sqrt(7*13) = RQ

QP = sqrt(26^2 - 364) = sqrt(676-364) = 2sqrt(78)