O is the center of a cicle AB=16cm,CD=14cm seg OT is perpendicular to seg AB seg ON is perpendicular to - Maths - Circles

Question

O is the center of a cicle AB=16cm,CD=14cm seg OT is
perpendicular to seg AB seg ON is perpendicular to seg CD If seg
OT=6cm then find ON

Aakash Sharma · Accepted Answer

Dear Student! Here is the answer to your query

Given : O is the centre of the circle and OT âŠ¥ AB and ON âŠ¥ CD also AB = 16 cm, ON = 14 cm and OT = 6 cm Construction : Join OA and OD We know that perpendicular from the length of the cirlce bisects the chord $\Rightarrow AT = \frac{1}{2} AB = \frac{1}{2} \times 16 cm = 8 cm and ND = \frac{1}{2} CD = \frac{1}{2} \times 14 cm = 7 cm$ In right Î”AOT AO2 = OT2 + AT2 (Pythagoras theorem) $\Rightarrow {AO}^{2} = 6^{2} + 8^{2} = 36 + 64 = 100 {cm}^{2} \Rightarrow AO = \sqrt{100} cm = 10 cm$ Also AO = DO = radius = 10 cm In Î”NOD OD2 = ON2 + ND2 â‡’ 102 = ON2 + 72 â‡’ ON2 = 102 â€“ 72 = 100 â€“ 49 = 51 cm2 $\Rightarrow ON = \sqrt{51} cm$ Cheers!

O is the center of a cicle AB=16cm,CD=14cm seg OT is perpendicular to seg AB seg ON is perpendicular to seg CD .If seg OT=6cm then find ON