Question

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Answer 1

Answer:

By Mid point theorem.

Step-by-step explanation:

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Answer 2

Answer:

As shown in the attached figure, AB is a chord of the circle with centre at 'O' and OD is perpendicular to AB.

We are to prove that CA = 2 OD, if BC is the diameter of the circle.

Since the perpendicular drawn from the centre to any chord of a circle divides the chord in two equal parts, so we have

which implies that 'D' is the mid-point of AB.

Also, Since BC is the diameter and a diameter is equal to twice the radius of the circle, so we have

CO = OB = half of BC.

Therefore, 'O' is the mid-point of BC.

We have the following Mid-Point Theorem, which states that

the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Now, in ΔABC, 'O' and 'D' are the mid-points of the sides BC and AB respectively, so by using the above Mid-Point Theorem, we have

OD is parallel to CA and OD is half of CA.

Thus,

od=1/2ca

Hence proved.

Step-by-step explanation:

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