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.

Because the tangent is perpendicular to the radius at the point of contact, triangle OBP is a right triangle with the right angle at B. In this triangle, OB is the radius of 6 cm, and the hypotenuse OP is given as 10 cm. The area of a right triangle is half the product of the perpendicular sides, which are OB and BP. Using the Pythagorean theorem, the length of BP is the square root of (OP squared minus OB squared), which is the square root of (100 minus 36), giving BP as 8 cm. Calculating the area gives 0.5 times 6 times 8, resulting in an area of 24 square cm.

• Thanks
• Wrong explanation