Maths Special 2021.10.21(2)

16. Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2).

Or

The line segment joining the points A (2,1) and B (5, - 8) is trisected at the point P and Q such that P is nearer to A. If P also lies on the line given by 2 x - y + k = 0, Find the value of k.

17. Prove that (sin A + cos A)2(square) + (cos A + sin A) 2(square) = 7 + tan2(square)A + cot2(square)A.

Or

Prove that (1 + cot A - cosec A)  (1 + tan A + sec A) = 2.

18. In figure 2, PQ is a chord of length 8 cm of circle of radius 5cm and centre O. The tangent at P and Q intersect at point P find the length of TP.

19. In figure 3 angle ACB equals to 90° and CD perpendicular AB. Prove that CD2(square) = BD × AD.

Or

If P and Q are the points on side CA and CB respectively of ∆ ABC right angled at C prove that AC2 (square) + PQ2 (square) = AB2 (square) + PQ2(square).

20. Find the area of the shaded region in figure 4, if ABCD is a rectangle with sides 8cm and 6cm and O is the centre of circle. (Take π =  3.14)