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Standard VII

Mathematics

Classification of Triangles Based on Angles

If D is the m...

Question

If D is the mid-point of the hypotenuse AC of a right-angled triangle ABC. prove that BD $= \frac{1}{2}$ AC.

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Solution

Area of triangle ABD = Area of trinagle BCD
$⟹ \frac{1}{2} D B . D A = \frac{1}{2} D B . D C$ $[$ Area of triangle $= \frac{1}{2} \times b \times h$ $]$
$⟹ D A = D C$
$∵$ Circumradius $R = \frac{A B \times B C \times A C}{4 △}$

$= \frac{A B \times B C \times A C}{4 \times \frac{1}{2} \times A B \times B C}$
$⟹ B D = R = \frac{A C}{2}$ $[∵$ Circumradius $(R) = B D]$

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If D is the mid-point of the hypotenuse AC of a right-angled triangle ABC. prove that BD=12 AC.

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If D is the mid-point of the hypotenuse AC of a right-angled triangle ABC. prove that BD $= \frac{1}{2}$ AC.