Question

A semicircle is drawn on AB as diameter. Let X be a point on AB.
From X, a perpendicular XM is drawn on AB cutting the semicircle at M.
Prove that AX. XB = MX^2.​

Answer 1

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Step-by-step explanation:

Angle in a semi-circle is a right angle.

∠ADC = 90°

CD2 = AC × CB

AC = 2 cm and CD = 6 cm

CB = 18 cm

Hence, AB = AC + CB = 20 cm

Radius of semicircle = 10 cm

Area of semi-circle = 1/2 * π * r2 = 50 π

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Answer 2

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Angle in a semi-circle is a right angle.

Angle in a semi-circle is a right angle.∠ADC = 90°

Angle in a semi-circle is a right angle.∠ADC = 90°CD2 = AC × CB

Angle in a semi-circle is a right angle.∠ADC = 90°CD2 = AC × CBAC = 2 cm and CD = 6 cm

Angle in a semi-circle is a right angle.∠ADC = 90°CD2 = AC × CBAC = 2 cm and CD = 6 cmCB = 18 cm

Angle in a semi-circle is a right angle.∠ADC = 90°CD2 = AC × CBAC = 2 cm and CD = 6 cmCB = 18 cmHence, AB = AC + CB = 20 cm

Angle in a semi-circle is a right angle.∠ADC = 90°CD2 = AC × CBAC = 2 cm and CD = 6 cmCB = 18 cmHence, AB = AC + CB = 20 cmRadius of semicircle = 10 cm

Angle in a semi-circle is a right angle.∠ADC = 90°CD2 = AC × CBAC = 2 cm and CD = 6 cmCB = 18 cmHence, AB = AC + CB = 20 cmRadius of semicircle = 10 cmArea of semi-circle = 1/2 * π * r2 = 50 π

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