In the figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Asked by Pragya Singh | 1 year ago |  85

##### Solution :-

Given here,

In ΔOPQ, AB || PQ

By using Basic Proportionality Theorem,

$$\dfrac{OA}{AP}=\dfrac{OB}{BQ}$$…………….(i)

Also given,

In ΔOPR, AC || PR

By using Basic Proportionality Theorem

$$\dfrac{OA}{AP}=\dfrac{OC}{CR}$$……………(ii)

From equation (i) and (ii), we get,

$$\dfrac{OB}{BQ}$$ = $$\dfrac{OC}{CR}$$

Therefore, by converse of Basic Proportionality Theorem,

In ΔOQR, BC || QR.

Answered by Abhisek | 1 year ago

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