Question

mathematics please answer​

Answer 1

Step-by-step explanation:

picture is blur so I can't answer

Answer 2

Step-by-step explanation:

Given:Figure

To find:

a) Write one pair of equal angle.

b)Prove that PA×PB=PC×PD

Solution:

Tip:

Use Secant rule;

It states that; In a circle,If two secants are drawn from one external point , then the product of the external segment and the total length of each secant are equal.

a: Write one pair of equal angle.

We know that, when two straight lines meet at a point 2 pairs of vertically opposite angles are formed.

Here,

AD and BC meets at M.

Thus,

$\bf \angle AMB=\angle DMC$

Another pair: We know that a chord make equal angle in same segment.

So, Chord BD makes two equal angles

$\bf \angle BAD=\angle DCB$

b: Prove that PA×PB=PC×PD

In ∆PBC and ∆PDA

$\angle PBC=\angle PDA$

[Angle formed by same arc in same segment of circle are equal]

$\angle BPC =\angle DPA$

[Common in both ∆'s]

From AA criteria of similarity $\bf ∆PBC \sim ∆PDA$

Thus, ratio's of corresponding sides are equal.

$\frac{PB}{PD}=\frac{PC}{PA}$

On cross multiplication

$PA\times PB=PC\times PD$

Alternatively:It can be proved by theorem discussed under tip section.

From external point P two secants are drawn, PB and PD.

Thus,the product of the external segment(PA and PC) and the total length of each secant are equal.

$\bf PA×PB=PC×PD$

Final answer:

1) $\bf \angle AMB=\angle DMC$

and

$\bf \angle BAD=\angle DCB$

2)PA×PB=PC×PD has been proved.

Hope it helps you.

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