( overline{J K} ) and ( overline{J L} ) are tangent to the circle. Find the length of ( overline{J L} ).

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Accepted Answer

Step:1 ：Let (O) be the center of the circle, (overline{J K} ) and ( overline{J L} ) are tangent to the circle at points (A) and (B), respectively.Step:2 ：By the tangent and radius theorem, (angle OAJ = angle OBL = 90^circ). Hence, (OJ) is the geometric mean of (JA) and (JL).Step:3 ：Apply the Pythagorean theorem to triangle (Delta OAJ): (OJ^2 = OA^2 - AJ^2)Step:4 ：Apply the Pythagorean theorem to triangle (Delta OBL): (OJ^2 = OB^2 - BL^2)Step:5 ：Set the two equations equal to each other: (OA^2 - AJ^2 = OB^2 - BL^2)Step:6 ：Plug in the given values: ((10)^2 - (8)^2 = (10)^2 - BL^2)Step:7 ：Solve the equation for (BL): (BL^2 = 36)Step:8 ：Take the square root to find the length of (overline{J L} ): (BL = sqrt{36})Step:9 ：Answer: (BL = 6)

Answer

Step: 1 ：Let (O) be the center of the circle, (overline{J K} ) and ( overline{J L} ) are tangent to the circle at points (A) and (B), respectively.Step: 2 ：By the tangent and radius theorem, (angle OAJ = angle OBL = 90^circ). Hence, (OJ) is the geometric mean of (JA) and (JL).Step: 3 ：Apply the Pythagorean theorem to triangle (Delta OAJ): (OJ^2 = OA^2 - AJ^2)Step: 4 ：Apply the Pythagorean theorem to triangle (Delta OBL): (OJ^2 = OB^2 - BL^2)Step: 5 ：Set the two equations equal to each other: (OA^2 - AJ^2 = OB^2 - BL^2)Step: 6 ：Plug in the given values: ((10)^2 - (8)^2 = (10)^2 - BL^2)Step: 7 ：Solve the equation for (BL): (BL^2 = 36)Step: 8 ：Take the square root to find the length of (overline{J L} ): (BL = sqrt{36})Step: 9 ：Answer: (BL = 6)

$\overset{―}{J K}$ and $\overset{―}{J L}$ are tangent to the circle. Find the length of $\overset{―}{J L}$ .

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Popular Problems

JK― and JL― are tangent to the circle. Find the length of JL―.

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Popular Problems

$\overset{―}{J K}$ and $\overset{―}{J L}$ are tangent to the circle. Find the length of $\overset{―}{J L}$ .