Mathematics
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 :
18 cm
27 cm
9 cm
none of these
Answer
Let tangent QR intersect circle at point D.
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.
Related Questions
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