D is a point on BC such that AD is the bisector of angleA. Show that:

angle ADC = 90 + $\frac{(angleB-angleC)}{2}$

angle ADC = 90 + $\frac{(angleB-angleC)}{2}$

Alex Baird
2022-07-28
Answered

D is a point on BC such that AD is the bisector of angleA. Show that:

angle ADC = 90 + $\frac{(angleB-angleC)}{2}$

angle ADC = 90 + $\frac{(angleB-angleC)}{2}$

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losnonamern

Answered 2022-07-29
Author has **12** answers

e know that

angle ADC = 180 - angle ADB

= 180 - [180 - angle B - angle BAD]

= angle B + angle BAD

= angle B + angle A/2 since AD is an angular bisector

= angle B + (90 - angle B/2 -angle C/2)

= angle B + 90 - angle B/2 -angle C/2

= 90 + angle B/2 -angle C/2

= 90 + (angle B - angle C)/2thus proved

angle ADC = 180 - angle ADB

= 180 - [180 - angle B - angle BAD]

= angle B + angle BAD

= angle B + angle A/2 since AD is an angular bisector

= angle B + (90 - angle B/2 -angle C/2)

= angle B + 90 - angle B/2 -angle C/2

= 90 + angle B/2 -angle C/2

= 90 + (angle B - angle C)/2thus proved

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It's been a while since I've had to do derivations so I'm just a little rusty. I need to understand the steps for deriving (Py – 2)(44 – 2Py + Px) to reach Py = 12 + 0.25Px. Py here is price of product y and Px is the price of product x.

I undertsant that I need to take product rule of the first equation and then set it = 0 and solve for Py, but it's finding that derived equation that's troubling me.

How I tried to do it was to first simplify the equation into 44Py - 2Py^2 + PxPy - 88 + 4Py + 2Px. Then taking the derivative and simplifying a little I end up with 46 - 3Py + Px which I would then set = 0 and solve for Py, giving me Py = (46 + Px)/3. Which is obviously not correct.

If you could help me through the steps to reach Py = 12 + 0.25Px I would be very greatful.

I undertsant that I need to take product rule of the first equation and then set it = 0 and solve for Py, but it's finding that derived equation that's troubling me.

How I tried to do it was to first simplify the equation into 44Py - 2Py^2 + PxPy - 88 + 4Py + 2Px. Then taking the derivative and simplifying a little I end up with 46 - 3Py + Px which I would then set = 0 and solve for Py, giving me Py = (46 + Px)/3. Which is obviously not correct.

If you could help me through the steps to reach Py = 12 + 0.25Px I would be very greatful.

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