Q7 of 65 Page 152

In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove that:

(i) Δ APC ~ Δ DPB


(ii) AP . PB = CP . DP


(i) In triangle APC and DPB,

∠CAP = ∠BDP (Angles on the same side of a chord are equal)


∠APC = ∠DPB (Opposite angles)


Hence,


Δ APC ~ Δ DPB (By AAA similarity)


(ii) Since, the two triangles are similar


Hence,



Or,


AP * PB = CP * DP


Hence, proved


More from this chapter

All 65 →
5

In Fig. 6.60, AD is a median of a triangle ABC and AM⊥ BC. Prove that:


(i)


(ii)


(iii)

6

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides

 8

In Fig. 6.62, two chords AB and CD of a circle intersect each other at the point P(when produced) outside the circle. Prove that

(i) Δ PAC ~ Δ PDB


(ii) PA . PB = PC . PD


 9

In Fig. 6.63, D is a point on side BC of Δ ABC such thatProve that AD is thebisector of ∠ BAC