Two circles intersect at C and D, and their common tangents intersect at T. CP and CQ are the tangents at C to the two circles; prove that CT bisects $\mathrm{\angle}PCQ$.

Liberty Page
2022-09-17
Answered

Two circles intersect at C and D, and their common tangents intersect at T. CP and CQ are the tangents at C to the two circles; prove that CT bisects $\mathrm{\angle}PCQ$.

You can still ask an expert for help

asked 2022-08-21

How to use congruence and angle bisector theorem for this geometry question involving isosceles triangle?

Here is the diagram for the question:

In triangle $\mathrm{\u25b3}ADC$, $|AB|=|AC|=8$ and $|NC|=6$. AN is the bisector of $\measuredangle BAC$. $\measuredangle ADC=2\cdot \measuredangle BCD$. $|DN|=x$. Find x.

Here is the diagram for the question:

In triangle $\mathrm{\u25b3}ADC$, $|AB|=|AC|=8$ and $|NC|=6$. AN is the bisector of $\measuredangle BAC$. $\measuredangle ADC=2\cdot \measuredangle BCD$. $|DN|=x$. Find x.

asked 2022-07-15

Let quadrilateral ABCD satisfy $\mathrm{\angle}BAC=\mathrm{\angle}CAD=2\phantom{\rule{thinmathspace}{0ex}}\mathrm{\angle}ACD={40}^{\circ}$ and $\mathrm{\angle}ACB={70}^{\circ}$. Find $\mathrm{\angle}ADB$.

asked 2022-09-19

Given a triangle $\mathrm{\u25b3}ABM$ such that $|AM|=|BM|$ and a point C such that the oriented angle $\mathrm{\angle}AMB$ has twice the size of $\mathrm{\angle}ACB$, show that $|CM|=|AM|$.

I am pretty sure that this must hold. Can somebody point me to an (elementary) proof?

I am pretty sure that this must hold. Can somebody point me to an (elementary) proof?

asked 2022-08-10

The point M is the internal point of the ABC equilateral triangle. Find the $\mathrm{\angle}BMC$ if $|MA{|}^{2}=|MB{|}^{2}+|MC{|}^{2}$.

asked 2022-08-24

One of the rays of the inscribed angle is the diameter.

Given: Circle O

BC is a diameter.

Prove: $m\mathrm{\angle}ACB=\frac{1}{2}mAB$

Given: Circle O

BC is a diameter.

Prove: $m\mathrm{\angle}ACB=\frac{1}{2}mAB$

asked 2022-07-27

An angle measures 15 more than twice it's supplement. find themeasure of it's supplement.

asked 2022-09-20

In $\mathrm{\Delta}ABC,$, K and L are points on BC. AL is the bisector of $\mathrm{\angle}KAC$. $KL\times BC=BK\times CL$. Find $\mathrm{\angle}BAL$.