In the figure PA, PB are tangents through A and B of a circle with cen

1.	In the figure PA, PB are tangents through A and B of a circle with center O. If the radius of the circle is r, then prove that OP × OQ = r2.
Answer» Δ OQA, ΔOPA are triangle with equal angles. The ratio of sides opposite to the equal angles. \(\frac{OA}{OP}=\frac{OQ}{OA}\,\)\(\Rightarrow \frac{r}{OP}=\frac{OQ}{r}\) \(r^2=OP\times OQ\) \(OP\times OQ=r^2\)

In the figure PA, PB are tangents through A and B of a circle with center O. If the radius of the circle is r, then prove that OP × OQ = r2.

Answer»

Δ OQA, ΔOPA are triangle with equal angles. The ratio of sides opposite to the equal angles.

\(\frac{OA}{OP}=\frac{OQ}{OA}\,\)\(\Rightarrow \frac{r}{OP}=\frac{OQ}{r}\)

\(r^2=OP\times OQ\)

\(OP\times OQ=r^2\)

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In the figure PA, PB are tangents through A and B of a circle with center O. If the radius of the circle is r, then prove that OP × OQ = r2.

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