Question
Download Solution PDFA tangent is drawn from a point M to a circle, which meets the circle at T such that MT = 12 cm. A secant MAB intersects the circle at points A and B. If MA = 8 cm, what is the length ( in cm ) of the chord AB?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A tangent is drawn from point M to a circle, which meets the circle at T such that MT = 12 cm.
A secant MAB intersects the circle at points A and B.
MA = 8 cm
Concept used:
If SUV and SW are a secant and a tangent respectively drawn from an external point S on a circle whose center is at C, then SU × SV = SW2
Calculation:
According to the concept,
MA × MB = MT2
⇒ 8 × MB = 122
⇒ MB = 144/8
⇒ MB = 18
⇒ MA + AB = 18
⇒ 8 + AB = 18
⇒ AB = 18 - 8
⇒ AB = 10
∴ The measure of AB is 10 cm.
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