CBSE 2026 · Region 5 · Set 3 · Q32

(a)

D is the mid-point of side BC of $\displaystyle \triangle \mathrm{ABC}$. CE and BF intersect at O, a point on AD . AD is produced to G such that $\displaystyle \mathrm{OD}=\mathrm{DG}$. Prove that

(i)

OBGC is a parallelogram.

(ii)

$\displaystyle \mathrm{EF}|\mid \mathrm{BC}$

(iii)

$\displaystyle \triangle \mathrm{AEF} \sim \triangle \mathrm{ABC}$

(iii)

(b)

Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that

(i)

$\displaystyle \mathrm{AQ}=\mathrm{QR}$

(ii)

$\displaystyle \mathrm{AP}=2 \mathrm{PQ}$

(iii)

$\displaystyle \mathrm{PR}=2 \mathrm{AP}$