In the given fig- find the perimeter of - ABC- if AP -10 cm

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Standard X

Mathematics

Tangent and Secant

In the given ...

Question

In the given fig, find the perimeter of $Δ$ ABC, if AP = 10 cm

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Solution

$∵$ BC touches the circle at R

$∵$ Tangents drawn from external point to the circle are equal

$∴$ AP = AQ, BR = BP & CR = CQ

$∴$ Perimeter of $Δ$ ABC = AB +BC +AC

= AB + BR +RC + AC

= AB + (BP + CQ) + AC

= (AB + BP) + (CQ + AC)

= AP + AQ

= 2AP

= 2(10)

= 20cm

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In the given fig, find the perimeter of ΔABC, if AP = 10 cm

∵BC touches the circle at R ∵Tangents drawn from external point to the circle are equal ∴AP = AQ, BR = BP & CR = CQ ∴Perimeter of ΔABC = AB +BC +AC = AB + BR +RC + AC = AB + (BP + CQ) + AC = (AB + BP) + (CQ + AC) = AP + AQ = 2AP = 2(10) = 20cm

In the given fig, find the perimeter of $Δ$ ABC, if AP = 10 cm

$∵$ BC touches the circle at R

$∵$ Tangents drawn from external point to the circle are equal

$∴$ AP = AQ, BR = BP & CR = CQ

$∴$ Perimeter of $Δ$ ABC = AB +BC +AC

= AB + BR +RC + AC

= AB + (BP + CQ) + AC

= (AB + BP) + (CQ + AC)

= AP + AQ

= 2AP

= 2(10)

= 20cm