Question

The circles with centre P,Q,R intersect at points B,C,D,E line CB and ED intersect at point m.lines drawn from point touch circle at points. A and F. prove MA=MF​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Explanation:

It is given that P, Q, R intersect at the points B,C,D,E line CB and ED intersect at point m.

Lines drawn from the point touch circle at points A and F

To prove that MA=MF​

Now, we shall consider the circle with center P.

From the figure, we can see that MA is a tangent and MC is secant.

By applying the tangent secant theorem, we get,

$M A^{2}=M B \times M C$ ------(1)

Let us consider the circle with center Q.

From the figure, we can see that MC and ME are the lines that intersect externally at the point M.

By applying the external dividion of chord theorem, we get,

$M C \times M B=M E \times M D$ ----------(2)

Let us consider the circle with center R.

From the figure, we can see that the MF is a tangent and ME is secant.

Again, by applying the tangent secant theorem, we get,

$M F^{2}=M D \times M E$ ------------(3)

Let us substitute the equations (1) and (3) in equation (2).

Thus, we have,

$M A^{2}=M F^{2}$

Taking square root on both sides of the equation, we get,

$M A=M F$

Hence proved.

Learn more:

(1) In the adjoining figure the circles with centre P,Q,R intersect at points B, C, D and E as shown. Line CB and line ED intersect at point M. Lines drawn from point M touch the circle at points A and F. Prove that MA=MF

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(2) In the given figure common tangents A B and C D to the two circle intersect at E. prove that a b is equal to CD

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