A) 6.5 cm
B) 7.2 cm
C) 7.6 cm
D) 8 cm
Correct Answer: D
Solution :
Let the two chords AB and CD of lengths \[16\text{ }cm\]and \[17\text{ }cm\] are drawn perpendicular to each other in a circle of radius \[10\text{ }cm.\]Their point of intersection is P. \[\therefore \] \[O{{M}^{2}}=O{{A}^{2}}-A{{M}^{2}}={{10}^{2}}-{{8}^{2}}=36\] \[O{{N}^{2}}=O{{C}^{2}}-C{{N}^{2}}\] \[={{10}^{2}}-{{(8.5)}^{2}}\] \[ON=\sqrt{100-2.25}\] \[=\sqrt{27.75}\] \[\therefore \]Required distance \[=OP=\sqrt{O{{M}^{2}}+O{{N}^{2}}}\] \[=\sqrt{36+27.75}\] \[=\sqrt{63.75}\] \[=8\,cms\] (approximately)You need to login to perform this action.
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