A BC D is a quadrilateral with side lengths A B = 4 , BC = 10 , C D = 6 and A D = 6 , and diagonal B D = 8 units. If the incircles of triangles A B D and BC D touch B D at P and Q respectively, then a

Question

A BC D is a quadrilateral with side lengths A B = 4 , BC = 10 , C D = 6 and A D = 6 , and diagonal B D = 8 units. If the incircles of triangles A B D and BC D touch B D at P and Q respectively, then area of quadrilateral C 1 ​ P C 2 ​ Q (where C 1 ​ and C 2 ​ are incentres of triangles A B D and BC D respectively), is

TestHub · Accepted Answer

For △ A B D , s = 9 , area = 3 15 ​ , so r 1 ​ = 15 ​ /3 and BP = s − A D = 3 . For △ BC D , s = 12 , area = 24 , so r 2 ​ = 2 and D Q = s − BC = 2 . Hence PQ = 8 − 3 − 2 = 3 , and the two right triangles forming the quadrilateral have total area 2 1 ​ ( r 1 ​ + r 2 ​ ) PQ = 3 + 15 ​ /2 .

Mathematics - Properties of Triangle Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main 2027 (Class 12+)