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Question
In the given figure, PT is a tangent to the circle at T, chord BA is produced to meet the tangent at P. Perpendicular BC bisects the chord TA at C. If PA = 9 cm and TB = 7 cm, find the lengths of:
- AB
- PT
Solution
Given: In diagram PT is tangent BC bisects TA at right angles.
BT = 7 cm, PA = 9 cm
(a) Line segment BC is a common side of both the ΔACB and ΔTCB.
ΔACB is 90° then ΔTCB also is 90°.
Hence the length of BT and the length of AB will be the same.
∴ Length of BT is 7 cm then length of AB is also 7 cm.
(b) PT2 = PA × PB
PT2 = 9 × (9 + 7)
PT2 = 9 × 16
PT = `sqrt(9 xx 16)`
PT = 3 × 4
PT = 4 cm
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