question_answer

Two chords of lengths 16 cm and 17 cm are drawn perpendicular to each other in a circle of radius 10 cm. The distance of their point of intersection from the centre is approximately

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)