Maths · Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre
Draw a circle with centre and radius Take a point outside the circle at a distan
Draw a circle with centre \( O \) and radius \( 6 \mathrm{cm} . \) Take a point \( P \) outside the circle at a distance of \( 10 \mathrm{cm} \) from \( 0 . \) Draw tangents to the circle from point \( P . \) Let the tangents intersect the circle in points \( A \) and \( B \). Find the area of triangle OBPin sq.cm.
- A. 24
- B. 26
- C. 25
- D. None of these
Step-by-step solution
Triangle OBP is right-angled at B because the radius is perpendicular to the tangent. Given OB = 6 cm and OP = 10 cm, by Pythagoras, BP = √(10² - 6²) = 8 cm. Area = (1/2) × OB × BP = (1/2) × 6 × 8 = 24 sq.cm.
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