Let A be the centre of the circle x2+y2 - 2x - 4y - 20 = 0. Suppose that the tangents at the points B(1, 7) and D(4, - 2) on the circle meet at the point C. The area of the quadrilateral ABCD is
A
75 sq. unit
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
145 sq. unit
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
150 sq. unit
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
50 sq. unit
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A 75 sq. unit Centre of the circle is A (1, 2) Equation of the tangent at B (1, 7) is y = 7 → (1) Equation of the tangent at D (4, - 2) is 3x - 4y - 20 = 0 → (2) Point of intersection of the lines (1) and (2) is C(16, 7) Area of ABCD=12∣∣∣(1−16)(2−7)(1−4)(7+2)∣∣∣=12∣∣∣−15−5−39∣∣∣=12|−135−15|=75