CBSE 2023 · Region 1 · Set 3 · Q34

(a)

Sides AB and AC and median AM of a $\displaystyle \triangle \mathrm{ABC}$ are proportional to sides DE and DF and Median DN of another $\displaystyle \triangle \mathrm{DEF}$. Show that $\displaystyle \triangle \mathrm{ABC}$ $\displaystyle \sim \triangle \mathrm{DEF}$.

(b)

ABCD is a parallelogram, P is a point on side BC and DP when produced meets AB produced at L. Prove that

(i)

$\displaystyle \frac{\mathrm{DP}}{\mathrm{PL}}=\frac{\mathrm{DC}}{\mathrm{BL}}$

(ii)

$\displaystyle \frac{\mathrm{DL}}{\mathrm{DP}}=\frac{\mathrm{AL}}{\mathrm{DC}}$

(iii)

If $\displaystyle \mathrm{LP}: \mathrm{PD}=2: 3$ then find $\displaystyle \mathrm{BP}: \mathrm{BC}$.

(iii)

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