Question 75

A and are two points on a circle with centre O. AT is a tangent, such that $$\angle$$BAT = $$45^\circ$$. is a point on OA, such that BN = 10 cm.The length of the median OM of the $$\triangle$$NOB is:

Solution

As AT is a tangent

∠OAT=90

Again ∠BAT=45

So, ∠OAB=90-45=45

△AOB, OA=OB

So, , ∠OAB=, ∠OBA=45

Then, , ∠NOB=180-45-45=90

And △BON is also right angled triangle.

Now, OM is a median of △BON,

Therefore, OM divides BN in two equal part

Hence, BM=MN=OM=5cm

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