In ΔABC, AB = AC. A circle drawn through B touches AC at D and intersect AB at P. If D is the mid point of AC and AP is 2.5 cm, then AB is equal to:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 10 cm.
| Understanding/Application |
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D is the mid-point of AC so,
AD = AC/2 But also given - AC = AB AD = AB/2 .....(1) |
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AD is a tangent and APB is a secant. So the tangent secant theorem can be applied - AD2 = AP × AB ⇒ (AB/2)2 = AP × AB ⇒ AB2/4 = 2.5 × AB ⇒ AB = 10 cm |
