Question

In the given figure AB = 9 cm, PA = 7.5 cm and PC = 5 cm.
Chords AD and BC intersect at P.
(0) Prove that APAB - APCD
9 cm
(ii) Find the length of CD.
(iii) Find area of APAB: area of APCD
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Answer 1

Answer:

Check out these images, for the solution.

Step-by-step explanation:

Answer 2

CORRECT QUESTION

In the given figure AB = 9 cm, PA = 7.5 cm and PC = 5 cm. Chords AD and BC intersect at P.

(i) Prove that ΔPAB ~ ΔPCD

(ii) Find the length of CD.

(iii) Find the area of ΔPAB: area of ΔPCD

ANSWER

The answers are as follows;

The answers are as follows; (i) ΔAPB ~ ΔPCD

The answers are as follows; (i) ΔAPB ~ ΔPCD (ii) DC = 6cm

The answers are as follows; (i) ΔAPB ~ ΔPCD (ii) DC = 6cm (iii) 2.25 : 1

GIVEN

AB = 9 cm, PA = 7.5 cm and PC = 5 cm. Chords AD and BC intersect at P.

TO FIND

(i) Prove that ΔPAB ~ ΔPCD

(ii) Find the length of CD.

(iii) Find the area of ΔPAB: area of ΔPCD

SOLUTION

PLEASE REFER TO THE IMAGE FOR THE FIGURE.

(i)

ΔPAB and ΔPCD

∠ABP = ∠CDP (Angles of same segment of the circle are equal)

Similarly,

∠PAB = ∠PCD

∠APB = ∠CPD (Vertically opposite angles are equal)

By A-A-A congruency criterion

ΔPAB ~ ΔPCD

Hence, Proved.

(ii)

It is known that sides of two similar traingles are in proportion.

Therefore,

BA/DC = PA/PC

9/DC = 7.5/5

DC = 6cm

(iii)

Area of ΔPAB and ΔPCD

It is known that

Ratio of areas of two similar triangles is proportional to the square of ratios of their corresponding sides.

Therefore,

(ΔPAB)ₐᵣₑₐ/(ΔPCD)ₐᵣₑₐ = (PA)²/(PC)²

= (7.5)²/(5²)

= 56.25 : 25

= 2.25 : 1

Hence, The answers are as follows;

Hence, The answers are as follows; (i) ΔAPB ~ ΔPCD

Hence, The answers are as follows; (i) ΔAPB ~ ΔPCD (ii) DC = 6cm

Hence, The answers are as follows; (i) ΔAPB ~ ΔPCD (ii) DC = 6cm (iii) 2.25 : 1

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