Two tangents are drawn to a circle from an external point A , they touch the circle at point B and C respectively. A third tangent intersects segments AB in P and AC in R and touch the circle at Q . If AB = 20 cm then the perimeter of the triangle APR is
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13
AB=AC=20 (tangents of a same circle from an external point are equal)
BP=PQ
CR=RQ
AB= AP+PB
=AP+PQ=20cm
AC=AR+CR
=AR+RQ= 20cm
Perimeter of triangle APR = AP+PR+AR
= AP+PQ+QR+AR
= AB+AC
=20+20cm
=40cm.
Hope it helps you!!!!!!!!!
Answered by
1
Perimeter of ΔAPR is 40 Units
Step-by-step explanation:
- Two tangents drawn from a point to a circle are congruent.
AB = AC, PB = PQ and QR = RC
Also, by symmetry of the figure,
PQ = QR
Let PB = PQ = QR = CR = x
As AB = 20, AP = AB – BP = 20 – x
AR = 20 – x
Perimeter of ΔAPR = AP + PR + AR (Sum of all Sides)
= 20 – x + 2x + 20 – x
= 40 units
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