Join OP and extend to Q such that OP : PQ = 2 : 1 Draw a line parallel to OA through Q.

It cuts OB at point M (say) take point D on OB such that M is mid point of OD joint DQ and Produce it to meet OA at N. Then by mid-point theorem, Q is mid point of DN. so OQ is median of

Δ ODN

As OP : PQ = 2 : 1,

P is centroid => DP : PC = 2 : 1

**Construction of OP : PQ = 2 : 1**

obtain mid-point L of OP.

with P as centre and radius PL, arc cuts OP produced at Q

**Construction of QM || OA :**

With O as centre, draw an arc to cut OQ at S_{1} and OA at SQ

With Q as centre and same radius, draw an arc to cut OQ at S_{3}

With S_{3} as centre and radius S_{1} S_{2}, draw an arc to cut previous arc at S_{4} join QS_{4}