Question

in the below figure from an external point A, tangents AB and AC are drawn to a circle PQ is a tangent to the circle at X. if AC=15cm,find the perimeter of the triangle APQ....
....plzz help in this question.

Answer 1

perimeter of circle will be 30 because AC = 15 and also =AB.

QC=QX and BP=PX (by theorm) therefor we can say AP+PX=15 and also AQ+QX= 15 thereofore perimeter of ∆APQ = 30

Answer 2

The perimeter of the triangle is 30cm.

Given:

Length of tangent AC = 15cm

To Find:

The perimeter of the triangle

Solution:

We use the property of tangents that says, the length of two tangents starting from the same point on the circle is equal.

Therefore, AB = AC = 15cm

Similarly, PB = PX and QX = QC

The perimeter of the triangle is the sum of its boundaries.

⇒ AP + PX + QX + AQ

⇒ (AP + PB) + (QC + AQ)

⇒ AB + AC

⇒ 15 + 15 = 30cm        (Ans.)

Therefore the perimeter of the triangle is 30cm.

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