Question

Draw a circle with centre $O$ and radius $6$ cm. Take a point $P$ outside the circle at a distance of $10$ cm from $O$. Draw tangents to the circle from point $P$. Let the tangents intersect the circle in points $A$ and $B$. Find the area of triangle $OBP$ in sq. cm.

• A. $24$
• B. $26$
• C. $25$
• D. None of these

Answer 1

The correct option is A $24$

In $△OBP$

$(OP{)}^2=(OB{)}^2+(BP{)}^{2}BP=\sqrt{(OP{)}^2-(OB{)}^2}BP=\sqrt{(10{)}^2-6^2}BP=\sqrt{64}=8cm$

Area $=\frac{1}{2}\times base\times height=\frac{1}{2}\times \left(OB\right)\times \left(BP\right)=\frac{1}{2}\times 6\times 8$

Area $=24c{m}^2$