Question

prove that op*oq=r^2

Answer 1

Heya,

We, can prove this by using the similarity criteria of the triangle.

Proof:
In triangle APO and triangle QAO

Angle OAP = Angle OQA. (each 90°)

Angle AOP = Angle AOQ (Common)

So,
triangle APO ~ triangle QAO

By applying BPT theorem, we get;

AO/QO = PO/AO

=> AO² = PO×QO

By the fig. we can see that AO I'd 'r'

So,
PO×QO = r²

Hence Proved.

Hope this helps...:)