A string art project is shown below. a ZQPS is a right angle because 8 + 15 > 16
R
8 centimeters
8 centimeters
b ZQPS is a right angle because 82 + 152 = 162
Р
S
15 centimeters
ZRSP is a right angle because 8 + 15 > 17
The piece of string that forms QS has a length of 16 centimeters.
The piece of string that forms PR has a length of 17 centimeters.
Which of the following statements is true?
d ZRSP is a right angle because 82 + 152 = 172

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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