In the given figure, the tangent from A touches the circle at B. BC is a diameter.

The Line AC cuts the circle at P. The tangent at P cuts AB at M. If $∠ P C B$ = $x^{\circ}$ , then $∠ B P M$ = ____.

$90^{\circ}$ - $x^{\circ}$

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$2 x^{\circ}$

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$x^{\circ}$

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$\frac{x^{\circ}}{2}$

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Solution

The correct option is C
$x^{\circ}$

Join PB. The figure thus looks like :

$∠ B P M$ = $∠ P C B$ = $x^{\circ}$ ......(Angles in alternate segment are equal)

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Similar questions

In the figure, the tangent from A touches the circle at B. BC is diameter. The line AC cuts the circle at P.

The tangent at P cuts AB at M. Which of the following options are correct?

Q. lf the tangent at

P

on the circle

x^{2} + y^{2} = a^{2}

cuts two parallel tangents of the circle at

A

and

B

then

P A . P B =

Q. In a right triangle

A B C

in which

∠ B = 90^{\circ},

a circle is drawn with

A B

as diameter intersecting the hypotenuse

A C

P

then tangent to the circle at

P

bisects B C.

In the given figure, PT is a common tangent to the circles touching externally at P and AB is another common tangent touching the circles at A and B. Prove that: [3 MARKS]

(i) T is the mid-point of AB

$(i i) ∠ A P B = 90^{\circ}$

(iii) If X and Y are centers of the two circles, show that the circle on AB as diameter touches the line XY.