two triangles bac and bad right angled at a and d are drawn on same base bc if - Maths - Triangles

Question

two triangles bac and bad right angled at a and d are drawn on
same base bc if ac and bd intersect at p prove that ap *
pc=bp*pd

Priyanka Kedia · Accepted Answer

$G i v e n : Δ B A C a n d Δ B A D a r e r i g h t a n g l e d a t A a n d D a n d A C a n d B D int e r \sec t a t p o int P . T o \Pr o v e : A P \times P C = B P \times P D \Pr o o f : I n Δ A P B a n d Δ D P C, ∠ A = ∠ D (e a c h 90^{0} g i v e n) ∠ A P B = ∠ D P C (v e r t i c a l l y o p p o s i t e a n g l e s) S o, Δ A P B \sim Δ D P C (b y A A s i m i l a r i t y) T h u s, \frac{A P}{B P} = \frac{P D}{P C} \Rightarrow A P \times P C = B P \times P D h e n c e p r o v e d .$

two triangles bac and bad right angled at a and d are drawn on same base bc . if ac and bd intersect at p . prove that ap * pc=bp*pd