Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
Let AB be a chord of circle with centre O.
Let AP and BP be two tangents at A and B respectively.
Suppose the tangents meet at point P. Join OP.
Suppose OP meets AB at C.
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q.
Since a line is intersecting Y-axis at P and X- axis at Q,
Coordinates of P = (0,y) and coordinates of Q = (x,0)
Let R be the midpoint of PQ.
For what value of n, are the nth terms of two A.Ps. 63, 65, 67,…. and 3, 10, 17,….. equal?
For A.P. 63, 65, 67,........, we have
First term = 63 and common difference = 65-63 = 2
Hence, nth term = an = 63 + (n-1) 2
For A.P. 3, 10, 17,........, we have
First term = 3 and common difference = 10-3 = 7
Hence, ntn term = an = 3 + (n-1) 7
If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.
In the figure, PA and PB are two tangents from an external point P to a circle with centre O and radius = a
What is the common difference of an A.P. in which a21- a7= 84?
Let a be the first term and d be the common difference of the given A.P.
The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?
Let the total number of rotten apples in a heap = n
Total number of apples in a heap = 900
probability of selecting a rotten apple from a heap = 0.18
If a tower 30 m high, casts a shadow 10 3m long on the ground, then what is the angle of elevation of the sun?
Let AB be the tower and BC be its shadow.
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8= 0 is 6 times the other.
If the distances of P(x, y) from A(5, 1) and B(-1, 5) are equal, then prove that 3x = 2y.
Given, P(x,y) is equidistant from A(5,1) and B(-1,5)
Now, AP = BP
A circle touches all the four sides of a quadrilateral ABCD. Prove that
AB + CD = BC + DA
Since tangents drawn from an external point to a circle are equal in length, we have
AP = AS ........(i)
BP = BQ ........(ii)
CR = CQ ........(iii)
DR = DS ........(iv)
Adding (i), (ii), (iii), (iv), we get
AP + BP + CR + DR = AS + BQ + CQ + DS
( AP + BP ) + ( CR + DR ) = ( AS + DS ) + ( BQ + CQ )