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In Delta ABC, AB = 1, BC = 1, and AC = 1...

In `Delta ABC, AB = 1, BC = 1, and AC = 1//sqrt2`. In `Delta MNP, MN =1, NP =1, and angle MNP = 2 angle ABC`. Find the side MP

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt7)/(2)`

In `Delta ABC, cos theta = (1 + 1-(1)/(2))/(2) = (3)/(4)`
`rArr cos 2 theta = 2 cos^(2) theta - 1= 2 xx (9)/(16) -1 = (1)/(8)`
In `Delta MNP, x^(2) = 1 + 1 - 2 cos 2 theta`
`= 2(1 - cos 2 theta) = 2 (1 - (1)/(8)) = (7)/(4)`
or `x = (sqrt7)/(2)`
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