Question

in figure , PR = 4cm and QR = 3cm . find AB + CD. ​

Answer 1

Answer:

14cm

Step-by-step explanation:

as the tangents from an external point are equal

PR=PB

PR=AP

so AB=AP+PB

AB=2PR=2*4=8cm

similarly

QR=QD and QR=QC

DC=2QR=2*3=6cm

AB+DC=8+6=14cm

Answer 2

AB + CD = 14 cm  

Given:

In figure, PR = 4 cm and QR = 3cm

To find:

Find AB + CD ​

Solution:

From the property of tangents, the length of two tangents drawn from an external point will we be equal

If we observe the given picture,

PB and PR are two tangents drawn from external point P on small circle

⇒ PB = PR ----(1)

PR and AP are two tangents drawn from point P on bigger circle

⇒ AP = PR ---- (2)

⇒ From figure, AB = AP + PB

⇒ AB = 2PR   [ From (1) and (2) ]

Given that PR = 4 cm

⇒  AB = 2(4) = 8 cm

⇒  AB = 8 cm ----(3)

Similarly

QR and QD are two tangents drawn from Q on small circle

⇒ QR = QD ------(4)

QR and QC are two tangents drawn from Q on bigger circle

⇒ QR = QC -----(5)

From figure DC = QC + QD  

⇒ CD = 2QR  [ From (4) and (5)

⇒ CD = 2(3)

⇒ CD = 6 cm -----(6)

From (3) and (6)

AB + CD ​ = 8 cm + 6 cm = 14 cm

⇒ AB + CD = 14 cm  

Therefore, AB + CD = 14 cm  

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