Q-3: If p, q are perpendiculars from the angular points A and B of the DABC drawn to any line
Through the vertex C then prove that
Let ÐACE = a clearly from fig we get
Q-4: Find the expression for area of cyclic quadrilateral.
Solution: A quadrilateral is cyclic quadrilateral if its vertices lie on a circle.
Let ABCD be a cyclic quadrilateral such that AB=a, BC=b, CD=c and DA=d.
Then ÐB+ÐD = 180 and ÐA+ÐC = 180
Let 2s = a+b+c+d be the perimeter of the quadrilateral.
Now, D = area of cyclic quadrilateral ABCD
= area of DABC + area of DACD
Using Cosine formula in a triangle ABC and ACD we have
Q-5: Find the distance between the circumcenter and incenter.
Let O be the circumcenter and I be the incenter of DABC. Let OF be perpendicular to AB and IE be perpendicular to AC and ÐOAF = 90-C.
\ÐOAI = ÐIAF-ÐOAF
Q-6: Prove that Where r = inradius, R=circum radius r1, r2, r3 are exradii.