A and B are two points on a circle with centre O. AT is a tangent, such that angel BAT = 45degree. N is a point on OA such than BN = 10 cm. The length of the median OM of the triangle NOB is?
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Step-by-step explanation:
Given A and B are two points on a circle with centre O. AT is a tangent, such that angel BAT = 45 degree. N is a point on OA such than BN = 10 cm
- Given AT is a tangent. With centre O, angle OAT = 90 degree
- Also angle BAT = 45 degree
- Now from angle OAB , OA = OB
- Angle OAB = 90 – 45 = 45 degree
- So angle OAB = angle OBA = 45 degree
- Since triangle NOB is a right angled triangle
- Now angle NOB = 180 – 45 – 45 = 90 degree
- In the right angled triangle BON, OM is the median.
- The median OM divides BN into two equal parts.
- Given BN = 10 cm
- Therefore BM = OM = 5 cm
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