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In the given figure, PA, PB and QR are tangents to a circle. If perimeter of the △PQR = 18 cm, the length of tangent PA is :

  1. 18 cm

  2. 27 cm

  3. 9 cm

  4. none of these

In the given figure, PA, PB and QR are tangents to a circle. If perimeter of the △PQR = 18 cm, the length of tangent PA is : Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

Let tangent QR intersect circle at point D.

In the given figure, PA, PB and QR are tangents to a circle. If perimeter of the △PQR = 18 cm, the length of tangent PA is : Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

Given,

Perimeter of the △PQR = 18 cm.

⇒ PQ + QD + RD + PR = 18 ………….(1)

We know that,

Two tangents drawn to a circle form an exterior point are equal in length.

∴ PA = PB = x (let), RD = RA and QD = QB.

Substituting above values in equation (1), we get :

⇒ PQ + QB + RA + PR = 18

⇒ PB + PA = 18

⇒ x + x = 18

⇒ 2x = 18

⇒ x = 9 cm.

∴ PA = 9 cm.

Hence, Option 3 is the correct option.

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