AS-level challenge question - circle geometry - tangents

A challenge question from the section on tangent and chord properties.
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/ @mathonify

[@Awai_quotes]

Thankyou so much for explaining this sir😊

[@mrmoleculeg3564]

sir for vector CM did u mean to write down (2,-1). As you had to go down by one unit.

[@mathonify]

Yes correct. Luckily it was a small side note

[@gutsmcgordan4184]

Thanks for explaining, however im still unsure on how you exactly found the P coordinate

[@mathonify]

From the centre (4,0) -> across 1 and up 2, gives you the point (5,2). If you want to do it algebraically, you could find the equation of QP and find where it intersects the circle. But that’s a much longer method.

[@gutsmcgordan4184]

@@mathonify ok then, ty again

[@elitepredator6719]

hello thanks a lot 🙃