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Question
In the given circle O is the centre of the circle and AD, AE are the two tangents. BC is also a tangent, then:
In the given circle O is the centre of the circle and AD, AE are the two tangents. BC is also a tangent, then:
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Solution
The correct option is D 2AE = AB + BC + AC
CD = CP and BE = BP, since tangents from the same point are always equal in length.
∴ AE = AD
Now, AD = AC + CD = AC + CP
and AE = AB + BE = AB + BP
∴ AE + AD = AC + CP + AB + BP
2AE = AC + AB + (CP + BP)
2AE = AB + AC + BC
2AE = AB + BC + AC
CD = CP and BE = BP, since tangents from the same point are always equal in length.
∴ AE = AD
Now, AD = AC + CD = AC + CP
and AE = AB + BE = AB + BP
∴ AE + AD = AC + CP + AB + BP
2AE = AC + AB + (CP + BP)
2AE = AB + AC + BC
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In the given circle, O is the centre and AD, AE are the two tangents. If BC is also a tangent, then prove that 2AE = AB + BC + AC
