Question

D
3. In the figure, PC = 16 cm,
CD = 18 cm, PA = 2PB
(a) What is the length of PD?
(b) Calculate the length of PA?C
lal PN - CD - CP
A​

Answer 1

Answer:

What is the length of CD if two chords AB and CD of a circle intersect each other at a point E outside the ... PA x PB = PD x PC ... The radius of two concentric circles are 13 cm and 8 cm.

Answer 2

The length of PD is 2 cm and length of PA is 8 cm.

Given - PC, CD and PA

Find - PD and PA

Solution - Firstly finding the length of PD.

So, here we can see the complete line CD measures 18 cm. It is divided into two sections PC and PC. We are given one part and are asked to find other part PD. This can be calculated simply through subtraction.

PD = CD - PC

Keep the values in equation to find the value of PD.

PD = 18 - 16

Performing subtraction

PD = 2 cm

Thus, the length of PD is 2 cm.

Now, finding the length of PA.

Using intersecting chord theorem, to find the length. As per the theorem, the product of sections on each chord are equal.

So, PD × PC = PA × PB

Keep the values in equation to find the value of PA.

2 × 16 = 2PB × PB

2PB² = 32

PB² = $\frac{32}{2}$

PB² = 16

PB = ✓16

PB = 4 cm

Calculating PA

PA = 2 × 4

PA = 8 cm

Therefore, PA measures 8 cm.

Hence, length of PD and PA is 2 cm and 8 cm respectively.

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