Question

If AB, AC, PQ are tangents in Fig. 10.51 and AB = 5 cm, find the perimeter of .

Answer 1

Answer:

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Answer 2

The question is incomplete here. The complete question is,

If AB, AC, PQ are tangents in Fig. 10.51 and AB = 5 cm, find the perimeter of Δ APQ.

Solution:

Let us assume the perimeter of ΔAPQ to be p.

The perimeter of a triangle is equal to the sum of its three sides.

Hence, p = AP + AQ + PQ

From the above figure, we get PQ = PX + XQ

By substituting this into the equation for p, we get

p = AP + AQ + PX + XQ

The two tangents drawn from an external point to a circle are equal in length.

Using the above property of a circle, we have

PX = PB

XQ = QC

By substituting these into the equation for p, we get

p = AP + AQ + PB + QC

p = (AP + PB) + (AQ + QC)

p = AB + AC        (from the above figure)

Using the same property of a circle as earlier, we have

AB = AC

Therefore, AC = 5 cm

Now, by substituting the values of AB and AC in the equation for p, we get

p = 5 + 5 = 10 cm

Hence, the perimeter of ΔAPQ is 10 cm.