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Question

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.


Solution

Given: In a right-angled ΔABCB=90o. D is the midpoint of hypotenuse AC. DB is joined.

To prove: BD = 12AC

Construction: Draw a circle with centre D and AC as diameter.

Proof: ABC=90o

The circle drawn on AC as diameter will pass through B.

BD is the radius of the circle.

But AC is the diameter of the circle and D is mid piont of AC.

AD = DC = BD

BD=12AC


Mathematics
RD Sharma
Standard IX

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