Solved: "To determine: Find x"

smileycellist2

Answered question

2021-08-13

To determine: Find x

SabadisO

Skilled2021-08-14Added 108 answers

the solution is written below

2021-12-13

In $△ H R U; H R^{2} = H U^{2} + U R^{2}$

[Pythagoria's Theorem]

$U R = \frac{1}{2} \times R S$ [A perpendicular radius bisects the chord]

$∴ U R \frac{1}{2} \times 14 = 7$

$∴ H R^{2} = H U^{2} + U R^{2} o r, H R^{2} = 8^{2} + 7^{2} = 113$

$H R = H Q$ [Radius of a circle are equal]

$∴ H R^{2} = H Q^{2} = 113$

In $△ H Q T; H Q^{2} = H T^{2} + T Q^{2}$ [Pythagoria's Theorem]

$113 = 8^{2} + T Q^{2}$

$∴ T Q^{2} = 113 - 64 = 49$

$∴ T Q = \sqrt{49} = 7$

$T Q = \frac{1}{2}$ of $P Q$ [A perpendicular radius bisects the chord]

$∴ P Q = 2 \times T Q = 2 \times 7 = 14$

But given $P Q = 3 x - 4$

$∴ 3 x - 4 = 14$

$∴ 3 x = 18$

$∴ x = 6$

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?